Changed fft4g to be built as C++

This CL changes so that the fft4g code is built as C++.

The CL also
-adds namespaces
-removes unused code.

To simplify the review, the CL is partitioned into different patchsets
where each comprising of one step in the modification of the code
(e.g., patch set 1 performs the renaming of the .c files to .cc).

Bug: webrtc:5298
Change-Id: I1dba78cc07c48622888be7b6f49a506795bc22ed
Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/171100
Reviewed-by: Ivo Creusen <ivoc@webrtc.org>
Reviewed-by: Henrik Lundin <henrik.lundin@webrtc.org>
Commit-Queue: Per Åhgren <peah@webrtc.org>
Cr-Commit-Position: refs/heads/master@{#30841}

4 files changed, 867 insertions, 1339 deletions

diff --git a/common_audio/third_party/fft4g/BUILD.gn b/common_audio/third_party/fft4g/BUILD.gn
index 789df92403..c7dd8f7108 100644
--- a/common_audio/third_party/fft4g/BUILD.gn
+++ b/common_audio/third_party/fft4g/BUILD.gn
@@ -10,7 +10,7 @@ import("../../../webrtc.gni")
 
 rtc_library("fft4g") {
   sources = [
-    "fft4g.c",
+    "fft4g.cc",
     "fft4g.h",
   ]
 }
diff --git a/common_audio/third_party/fft4g/fft4g.c b/common_audio/third_party/fft4g/fft4g.c
deleted file mode 100644
index 9cf7b9f6ca..0000000000
--- a/common_audio/third_party/fft4g/fft4g.c
+++ /dev/null
@@ -1,1332 +0,0 @@
-/*
- * http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
- * 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.
- *
- * Changes:
- * Trivial type modifications by the WebRTC authors.
- */
-
-/*
-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, float *, int *, float *);
-    void rdft(size_t, int, float *, size_t *, float *);
-    void ddct(int, int, float *, int *, float *);
-    void ddst(int, int, float *, int *, float *);
-    void dfct(int, float *, float *, int *, float *);
-    void dfst(int, float *, float *, int *, float *);
-
-
--------- 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 (float *)
-                        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 (float *)
-                        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 (size_t)
-                        n >= 2, n = power of 2
-        a[0...n-1]     :input/output data (float *)
-                        <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 (size_t *)
-                        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 (float *)
-                        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 (float *)
-                        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 (float *)
-                        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 (float *)
-                        <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 (float *)
-                        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 (float *)
-                        output data
-                            a[k] = C[k], 0<=k<=n
-        t[0...n/2]     :work area (float *)
-        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 (float *)
-                        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 (float *)
-                        output data
-                            a[k] = S[k], 0<k<n
-                        (a[0] is used for work area)
-        t[0...n/2-1]   :work area (float *)
-        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 (float *)
-                        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.
-*/
-
-#include <stddef.h>
-
-static void makewt(size_t nw, size_t *ip, float *w);
-static void makect(size_t nc, size_t *ip, float *c);
-static void bitrv2(size_t n, size_t *ip, float *a);
-#if 0  // Not used.
-static void bitrv2conj(int n, int *ip, float *a);
-#endif
-static void cftfsub(size_t n, float *a, float *w);
-static void cftbsub(size_t n, float *a, float *w);
-static void cft1st(size_t n, float *a, float *w);
-static void cftmdl(size_t n, size_t l, float *a, float *w);
-static void rftfsub(size_t n, float *a, size_t nc, float *c);
-static void rftbsub(size_t n, float *a, size_t nc, float *c);
-#if 0  // Not used.
-static void dctsub(int n, float *a, int nc, float *c)
-static void dstsub(int n, float *a, int nc, float *c)
-#endif
-
-
-#if 0  // Not used.
-void WebRtc_cdft(int n, int isgn, float *a, int *ip, float *w)
-{
-    if (n > (ip[0] << 2)) {
-        makewt(n >> 2, ip, w);
-    }
-    if (n > 4) {
-        if (isgn >= 0) {
-            bitrv2(n, ip + 2, a);
-            cftfsub(n, a, w);
-        } else {
-            bitrv2conj(n, ip + 2, a);
-            cftbsub(n, a, w);
-        }
-    } else if (n == 4) {
-        cftfsub(n, a, w);
-    }
-}
-#endif
-
-
-void WebRtc_rdft(size_t n, int isgn, float *a, size_t *ip, float *w)
-{
-    size_t nw, nc;
-    float xi;
-
-    nw = ip[0];
-    if (n > (nw << 2)) {
-        nw = n >> 2;
-        makewt(nw, ip, w);
-    }
-    nc = ip[1];
-    if (n > (nc << 2)) {
-        nc = n >> 2;
-        makect(nc, ip, w + nw);
-    }
-    if (isgn >= 0) {
-        if (n > 4) {
-            bitrv2(n, ip + 2, a);
-            cftfsub(n, a, w);
-            rftfsub(n, a, nc, w + nw);
-        } else if (n == 4) {
-            cftfsub(n, a, w);
-        }
-        xi = a[0] - a[1];
-        a[0] += a[1];
-        a[1] = xi;
-    } else {
-        a[1] = 0.5f * (a[0] - a[1]);
-        a[0] -= a[1];
-        if (n > 4) {
-            rftbsub(n, a, nc, w + nw);
-            bitrv2(n, ip + 2, a);
-            cftbsub(n, a, w);
-        } else if (n == 4) {
-            cftfsub(n, a, w);
-        }
-    }
-}
-
-#if 0  // Not used.
-static void ddct(int n, int isgn, float *a, int *ip, float *w)
-{
-    int j, nw, nc;
-    float xr;
-
-    nw = ip[0];
-    if (n > (nw << 2)) {
-        nw = n >> 2;
-        makewt(nw, ip, w);
-    }
-    nc = ip[1];
-    if (n > nc) {
-        nc = n;
-        makect(nc, ip, w + nw);
-    }
-    if (isgn < 0) {
-        xr = a[n - 1];
-        for (j = n - 2; j >= 2; j -= 2) {
-            a[j + 1] = a[j] - a[j - 1];
-            a[j] += a[j - 1];
-        }
-        a[1] = a[0] - xr;
-        a[0] += xr;
-        if (n > 4) {
-            rftbsub(n, a, nc, w + nw);
-            bitrv2(n, ip + 2, a);
-            cftbsub(n, a, w);
-        } else if (n == 4) {
-            cftfsub(n, a, w);
-        }
-    }
-    dctsub(n, a, nc, w + nw);
-    if (isgn >= 0) {
-        if (n > 4) {
-            bitrv2(n, ip + 2, a);
-            cftfsub(n, a, w);
-            rftfsub(n, a, nc, w + nw);
-        } else if (n == 4) {
-            cftfsub(n, a, w);
-        }
-        xr = a[0] - a[1];
-        a[0] += a[1];
-        for (j = 2; j < n; j += 2) {
-            a[j - 1] = a[j] - a[j + 1];
-            a[j] += a[j + 1];
-        }
-        a[n - 1] = xr;
-    }
-}
-
-
-static void ddst(int n, int isgn, float *a, int *ip, float *w)
-{
-    int j, nw, nc;
-    float xr;
-
-    nw = ip[0];
-    if (n > (nw << 2)) {
-        nw = n >> 2;
-        makewt(nw, ip, w);
-    }
-    nc = ip[1];
-    if (n > nc) {
-        nc = n;
-        makect(nc, ip, w + nw);
-    }
-    if (isgn < 0) {
-        xr = a[n - 1];
-        for (j = n - 2; j >= 2; j -= 2) {
-            a[j + 1] = -a[j] - a[j - 1];
-            a[j] -= a[j - 1];
-        }
-        a[1] = a[0] + xr;
-        a[0] -= xr;
-        if (n > 4) {
-            rftbsub(n, a, nc, w + nw);
-            bitrv2(n, ip + 2, a);
-            cftbsub(n, a, w);
-        } else if (n == 4) {
-            cftfsub(n, a, w);
-        }
-    }
-    dstsub(n, a, nc, w + nw);
-    if (isgn >= 0) {
-        if (n > 4) {
-            bitrv2(n, ip + 2, a);
-            cftfsub(n, a, w);
-            rftfsub(n, a, nc, w + nw);
-        } else if (n == 4) {
-            cftfsub(n, a, w);
-        }
-        xr = a[0] - a[1];
-        a[0] += a[1];
-        for (j = 2; j < n; j += 2) {
-            a[j - 1] = -a[j] - a[j + 1];
-            a[j] -= a[j + 1];
-        }
-        a[n - 1] = -xr;
-    }
-}
-
-
-static void dfct(int n, float *a, float *t, int *ip, float *w)
-{
-    int j, k, l, m, mh, nw, nc;
-    float xr, xi, yr, yi;
-
-    nw = ip[0];
-    if (n > (nw << 3)) {
-        nw = n >> 3;
-        makewt(nw, ip, w);
-    }
-    nc = ip[1];
-    if (n > (nc << 1)) {
-        nc = n >> 1;
-        makect(nc, ip, w + nw);
-    }
-    m = n >> 1;
-    yi = a[m];
-    xi = a[0] + a[n];
-    a[0] -= a[n];
-    t[0] = xi - yi;
-    t[m] = xi + yi;
-    if (n > 2) {
-        mh = m >> 1;
-        for (j = 1; j < mh; j++) {
-            k = m - j;
-            xr = a[j] - a[n - j];
-            xi = a[j] + a[n - j];
-            yr = a[k] - a[n - k];
-            yi = a[k] + a[n - k];
-            a[j] = xr;
-            a[k] = yr;
-            t[j] = xi - yi;
-            t[k] = xi + yi;
-        }
-        t[mh] = a[mh] + a[n - mh];
-        a[mh] -= a[n - mh];
-        dctsub(m, a, nc, w + nw);
-        if (m > 4) {
-            bitrv2(m, ip + 2, a);
-            cftfsub(m, a, w);
-            rftfsub(m, a, nc, w + nw);
-        } else if (m == 4) {
-            cftfsub(m, a, w);
-        }
-        a[n - 1] = a[0] - a[1];
-        a[1] = a[0] + a[1];
-        for (j = m - 2; j >= 2; j -= 2) {
-            a[2 * j + 1] = a[j] + a[j + 1];
-            a[2 * j - 1] = a[j] - a[j + 1];
-        }
-        l = 2;
-        m = mh;
-        while (m >= 2) {
-            dctsub(m, t, nc, w + nw);
-            if (m > 4) {
-                bitrv2(m, ip + 2, t);
-                cftfsub(m, t, w);
-                rftfsub(m, t, nc, w + nw);
-            } else if (m == 4) {
-                cftfsub(m, t, w);
-            }
-            a[n - l] = t[0] - t[1];
-            a[l] = t[0] + t[1];
-            k = 0;
-            for (j = 2; j < m; j += 2) {
-                k += l << 2;
-                a[k - l] = t[j] - t[j + 1];
-                a[k + l] = t[j] + t[j + 1];
-            }
-            l <<= 1;
-            mh = m >> 1;
-            for (j = 0; j < mh; j++) {
-                k = m - j;
-                t[j] = t[m + k] - t[m + j];
-                t[k] = t[m + k] + t[m + j];
-            }
-            t[mh] = t[m + mh];
-            m = mh;
-        }
-        a[l] = t[0];
-        a[n] = t[2] - t[1];
-        a[0] = t[2] + t[1];
-    } else {
-        a[1] = a[0];
-        a[2] = t[0];
-        a[0] = t[1];
-    }
-}
-
-static void dfst(int n, float *a, float *t, int *ip, float *w)
-{
-    int j, k, l, m, mh, nw, nc;
-    float xr, xi, yr, yi;
-
-    nw = ip[0];
-    if (n > (nw << 3)) {
-        nw = n >> 3;
-        makewt(nw, ip, w);
-    }
-    nc = ip[1];
-    if (n > (nc << 1)) {
-        nc = n >> 1;
-        makect(nc, ip, w + nw);
-    }
-    if (n > 2) {
-        m = n >> 1;
-        mh = m >> 1;
-        for (j = 1; j < mh; j++) {
-            k = m - j;
-            xr = a[j] + a[n - j];
-            xi = a[j] - a[n - j];
-            yr = a[k] + a[n - k];
-            yi = a[k] - a[n - k];
-            a[j] = xr;
-            a[k] = yr;
-            t[j] = xi + yi;
-            t[k] = xi - yi;
-        }
-        t[0] = a[mh] - a[n - mh];
-        a[mh] += a[n - mh];
-        a[0] = a[m];
-        dstsub(m, a, nc, w + nw);
-        if (m > 4) {
-            bitrv2(m, ip + 2, a);
-            cftfsub(m, a, w);
-            rftfsub(m, a, nc, w + nw);
-        } else if (m == 4) {
-            cftfsub(m, a, w);
-        }
-        a[n - 1] = a[1] - a[0];
-        a[1] = a[0] + a[1];
-        for (j = m - 2; j >= 2; j -= 2) {
-            a[2 * j + 1] = a[j] - a[j + 1];
-            a[2 * j - 1] = -a[j] - a[j + 1];
-        }
-        l = 2;
-        m = mh;
-        while (m >= 2) {
-            dstsub(m, t, nc, w + nw);
-            if (m > 4) {
-                bitrv2(m, ip + 2, t);
-                cftfsub(m, t, w);
-                rftfsub(m, t, nc, w + nw);
-            } else if (m == 4) {
-                cftfsub(m, t, w);
-            }
-            a[n - l] = t[1] - t[0];
-            a[l] = t[0] + t[1];
-            k = 0;
-            for (j = 2; j < m; j += 2) {
-                k += l << 2;
-                a[k - l] = -t[j] - t[j + 1];
-                a[k + l] = t[j] - t[j + 1];
-            }
-            l <<= 1;
-            mh = m >> 1;
-            for (j = 1; j < mh; j++) {
-                k = m - j;
-                t[j] = t[m + k] + t[m + j];
-                t[k] = t[m + k] - t[m + j];
-            }
-            t[0] = t[m + mh];
-            m = mh;
-        }
-        a[l] = t[0];
-    }
-    a[0] = 0;
-}
-#endif  // Not used.
-
-
-/* -------- initializing routines -------- */
-
-
-#include <math.h>
-
-static void makewt(size_t nw, size_t *ip, float *w)
-{
-    size_t j, nwh;
-    float delta, x, y;
-
-    ip[0] = nw;
-    ip[1] = 1;
-    if (nw > 2) {
-        nwh = nw >> 1;
-        delta = atanf(1.0f) / nwh;
-        w[0] = 1;
-        w[1] = 0;
-        w[nwh] = (float)cos(delta * nwh);
-        w[nwh + 1] = w[nwh];
-        if (nwh > 2) {
-            for (j = 2; j < nwh; j += 2) {
-                x = (float)cos(delta * j);
-                y = (float)sin(delta * j);
-                w[j] = x;
-                w[j + 1] = y;
-                w[nw - j] = y;
-                w[nw - j + 1] = x;
-            }
-            bitrv2(nw, ip + 2, w);
-        }
-    }
-}
-
-
-static void makect(size_t nc, size_t *ip, float *c)
-{
-    size_t j, nch;
-    float delta;
-
-    ip[1] = nc;
-    if (nc > 1) {
-        nch = nc >> 1;
-        delta = atanf(1.0f) / nch;
-        c[0] = (float)cos(delta * nch);
-        c[nch] = 0.5f * c[0];
-        for (j = 1; j < nch; j++) {
-            c[j] = 0.5f * (float)cos(delta * j);
-            c[nc - j] = 0.5f * (float)sin(delta * j);
-        }
-    }
-}
-
-
-/* -------- child routines -------- */
-
-
-static void bitrv2(size_t n, size_t *ip, float *a)
-{
-    size_t j, j1, k, k1, l, m, m2;
-    float xr, xi, yr, yi;
-
-    ip[0] = 0;
-    l = n;
-    m = 1;
-    while ((m << 3) < l) {
-        l >>= 1;
-        for (j = 0; j < m; j++) {
-            ip[m + j] = ip[j] + l;
-        }
-        m <<= 1;
-    }
-    m2 = 2 * m;
-    if ((m << 3) == l) {
-        for (k = 0; k < m; k++) {
-            for (j = 0; j < k; j++) {
-                j1 = 2 * j + ip[k];
-                k1 = 2 * k + ip[j];
-                xr = a[j1];
-                xi = a[j1 + 1];
-                yr = a[k1];
-                yi = a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 += 2 * m2;
-                xr = a[j1];
-                xi = a[j1 + 1];
-                yr = a[k1];
-                yi = a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 -= m2;
-                xr = a[j1];
-                xi = a[j1 + 1];
-                yr = a[k1];
-                yi = a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 += 2 * m2;
-                xr = a[j1];
-                xi = a[j1 + 1];
-                yr = a[k1];
-                yi = a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-            }
-            j1 = 2 * k + m2 + ip[k];
-            k1 = j1 + m2;
-            xr = a[j1];
-            xi = a[j1 + 1];
-            yr = a[k1];
-            yi = a[k1 + 1];
-            a[j1] = yr;
-            a[j1 + 1] = yi;
-            a[k1] = xr;
-            a[k1 + 1] = xi;
-        }
-    } else {
-        for (k = 1; k < m; k++) {
-            for (j = 0; j < k; j++) {
-                j1 = 2 * j + ip[k];
-                k1 = 2 * k + ip[j];
-                xr = a[j1];
-                xi = a[j1 + 1];
-                yr = a[k1];
-                yi = a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 += m2;
-                xr = a[j1];
-                xi = a[j1 + 1];
-                yr = a[k1];
-                yi = a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-            }
-        }
-    }
-}
-
-#if 0  // Not used.
-static void bitrv2conj(int n, int *ip, float *a)
-{
-    int j, j1, k, k1, l, m, m2;
-    float xr, xi, yr, yi;
-
-    ip[0] = 0;
-    l = n;
-    m = 1;
-    while ((m << 3) < l) {
-        l >>= 1;
-        for (j = 0; j < m; j++) {
-            ip[m + j] = ip[j] + l;
-        }
-        m <<= 1;
-    }
-    m2 = 2 * m;
-    if ((m << 3) == l) {
-        for (k = 0; k < m; k++) {
-            for (j = 0; j < k; j++) {
-                j1 = 2 * j + ip[k];
-                k1 = 2 * k + ip[j];
-                xr = a[j1];
-                xi = -a[j1 + 1];
-                yr = a[k1];
-                yi = -a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 += 2 * m2;
-                xr = a[j1];
-                xi = -a[j1 + 1];
-                yr = a[k1];
-                yi = -a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 -= m2;
-                xr = a[j1];
-                xi = -a[j1 + 1];
-                yr = a[k1];
-                yi = -a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 += 2 * m2;
-                xr = a[j1];
-                xi = -a[j1 + 1];
-                yr = a[k1];
-                yi = -a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-            }
-            k1 = 2 * k + ip[k];
-            a[k1 + 1] = -a[k1 + 1];
-            j1 = k1 + m2;
-            k1 = j1 + m2;
-            xr = a[j1];
-            xi = -a[j1 + 1];
-            yr = a[k1];
-            yi = -a[k1 + 1];
-            a[j1] = yr;
-            a[j1 + 1] = yi;
-            a[k1] = xr;
-            a[k1 + 1] = xi;
-            k1 += m2;
-            a[k1 + 1] = -a[k1 + 1];
-        }
-    } else {
-        a[1] = -a[1];
-        a[m2 + 1] = -a[m2 + 1];
-        for (k = 1; k < m; k++) {
-            for (j = 0; j < k; j++) {
-                j1 = 2 * j + ip[k];
-                k1 = 2 * k + ip[j];
-                xr = a[j1];
-                xi = -a[j1 + 1];
-                yr = a[k1];
-                yi = -a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-                j1 += m2;
-                k1 += m2;
-                xr = a[j1];
-                xi = -a[j1 + 1];
-                yr = a[k1];
-                yi = -a[k1 + 1];
-                a[j1] = yr;
-                a[j1 + 1] = yi;
-                a[k1] = xr;
-                a[k1 + 1] = xi;
-            }
-            k1 = 2 * k + ip[k];
-            a[k1 + 1] = -a[k1 + 1];
-            a[k1 + m2 + 1] = -a[k1 + m2 + 1];
-        }
-    }
-}
-#endif
-
-static void cftfsub(size_t n, float *a, float *w)
-{
-    size_t j, j1, j2, j3, l;
-    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
-    l = 2;
-    if (n > 8) {
-        cft1st(n, a, w);
-        l = 8;
-        while ((l << 2) < n) {
-            cftmdl(n, l, a, w);
-            l <<= 2;
-        }
-    }
-    if ((l << 2) == n) {
-        for (j = 0; j < l; j += 2) {
-            j1 = j + l;
-            j2 = j1 + l;
-            j3 = j2 + l;
-            x0r = a[j] + a[j1];
-            x0i = a[j + 1] + a[j1 + 1];
-            x1r = a[j] - a[j1];
-            x1i = a[j + 1] - a[j1 + 1];
-            x2r = a[j2] + a[j3];
-            x2i = a[j2 + 1] + a[j3 + 1];
-            x3r = a[j2] - a[j3];
-            x3i = a[j2 + 1] - a[j3 + 1];
-            a[j] = x0r + x2r;
-            a[j + 1] = x0i + x2i;
-            a[j2] = x0r - x2r;
-            a[j2 + 1] = x0i - x2i;
-            a[j1] = x1r - x3i;
-            a[j1 + 1] = x1i + x3r;
-            a[j3] = x1r + x3i;
-            a[j3 + 1] = x1i - x3r;
-        }
-    } else {
-        for (j = 0; j < l; j += 2) {
-            j1 = j + l;
-            x0r = a[j] - a[j1];
-            x0i = a[j + 1] - a[j1 + 1];
-            a[j] += a[j1];
-            a[j + 1] += a[j1 + 1];
-            a[j1] = x0r;
-            a[j1 + 1] = x0i;
-        }
-    }
-}
-
-
-static void cftbsub(size_t n, float *a, float *w)
-{
-    size_t j, j1, j2, j3, l;
-    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
-    l = 2;
-    if (n > 8) {
-        cft1st(n, a, w);
-        l = 8;
-        while ((l << 2) < n) {
-            cftmdl(n, l, a, w);
-            l <<= 2;
-        }
-    }
-    if ((l << 2) == n) {
-        for (j = 0; j < l; j += 2) {
-            j1 = j + l;
-            j2 = j1 + l;
-            j3 = j2 + l;
-            x0r = a[j] + a[j1];
-            x0i = -a[j + 1] - a[j1 + 1];
-            x1r = a[j] - a[j1];
-            x1i = -a[j + 1] + a[j1 + 1];
-            x2r = a[j2] + a[j3];
-            x2i = a[j2 + 1] + a[j3 + 1];
-            x3r = a[j2] - a[j3];
-            x3i = a[j2 + 1] - a[j3 + 1];
-            a[j] = x0r + x2r;
-            a[j + 1] = x0i - x2i;
-            a[j2] = x0r - x2r;
-            a[j2 + 1] = x0i + x2i;
-            a[j1] = x1r - x3i;
-            a[j1 + 1] = x1i - x3r;
-            a[j3] = x1r + x3i;
-            a[j3 + 1] = x1i + x3r;
-        }
-    } else {
-        for (j = 0; j < l; j += 2) {
-            j1 = j + l;
-            x0r = a[j] - a[j1];
-            x0i = -a[j + 1] + a[j1 + 1];
-            a[j] += a[j1];
-            a[j + 1] = -a[j + 1] - a[j1 + 1];
-            a[j1] = x0r;
-            a[j1 + 1] = x0i;
-        }
-    }
-}
-
-
-static void cft1st(size_t n, float *a, float *w)
-{
-    size_t j, k1, k2;
-    float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
-    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
-    x0r = a[0] + a[2];
-    x0i = a[1] + a[3];
-    x1r = a[0] - a[2];
-    x1i = a[1] - a[3];
-    x2r = a[4] + a[6];
-    x2i = a[5] + a[7];
-    x3r = a[4] - a[6];
-    x3i = a[5] - a[7];
-    a[0] = x0r + x2r;
-    a[1] = x0i + x2i;
-    a[4] = x0r - x2r;
-    a[5] = x0i - x2i;
-    a[2] = x1r - x3i;
-    a[3] = x1i + x3r;
-    a[6] = x1r + x3i;
-    a[7] = x1i - x3r;
-    wk1r = w[2];
-    x0r = a[8] + a[10];
-    x0i = a[9] + a[11];
-    x1r = a[8] - a[10];
-    x1i = a[9] - a[11];
-    x2r = a[12] + a[14];
-    x2i = a[13] + a[15];
-    x3r = a[12] - a[14];
-    x3i = a[13] - a[15];
-    a[8] = x0r + x2r;
-    a[9] = x0i + x2i;
-    a[12] = x2i - x0i;
-    a[13] = x0r - x2r;
-    x0r = x1r - x3i;
-    x0i = x1i + x3r;
-    a[10] = wk1r * (x0r - x0i);
-    a[11] = wk1r * (x0r + x0i);
-    x0r = x3i + x1r;
-    x0i = x3r - x1i;
-    a[14] = wk1r * (x0i - x0r);
-    a[15] = wk1r * (x0i + x0r);
-    k1 = 0;
-    for (j = 16; j < n; j += 16) {
-        k1 += 2;
-        k2 = 2 * k1;
-        wk2r = w[k1];
-        wk2i = w[k1 + 1];
-        wk1r = w[k2];
-        wk1i = w[k2 + 1];
-        wk3r = wk1r - 2 * wk2i * wk1i;
-        wk3i = 2 * wk2i * wk1r - wk1i;
-        x0r = a[j] + a[j + 2];
-        x0i = a[j + 1] + a[j + 3];
-        x1r = a[j] - a[j + 2];
-        x1i = a[j + 1] - a[j + 3];
-        x2r = a[j + 4] + a[j + 6];
-        x2i = a[j + 5] + a[j + 7];
-        x3r = a[j + 4] - a[j + 6];
-        x3i = a[j + 5] - a[j + 7];
-        a[j] = x0r + x2r;
-        a[j + 1] = x0i + x2i;
-        x0r -= x2r;
-        x0i -= x2i;
-        a[j + 4] = wk2r * x0r - wk2i * x0i;
-        a[j + 5] = wk2r * x0i + wk2i * x0r;
-        x0r = x1r - x3i;
-        x0i = x1i + x3r;
-        a[j + 2] = wk1r * x0r - wk1i * x0i;
-        a[j + 3] = wk1r * x0i + wk1i * x0r;
-        x0r = x1r + x3i;
-        x0i = x1i - x3r;
-        a[j + 6] = wk3r * x0r - wk3i * x0i;
-        a[j + 7] = wk3r * x0i + wk3i * x0r;
-        wk1r = w[k2 + 2];
-        wk1i = w[k2 + 3];
-        wk3r = wk1r - 2 * wk2r * wk1i;
-        wk3i = 2 * wk2r * wk1r - wk1i;
-        x0r = a[j + 8] + a[j + 10];
-        x0i = a[j + 9] + a[j + 11];
-        x1r = a[j + 8] - a[j + 10];
-        x1i = a[j + 9] - a[j + 11];
-        x2r = a[j + 12] + a[j + 14];
-        x2i = a[j + 13] + a[j + 15];
-        x3r = a[j + 12] - a[j + 14];
-        x3i = a[j + 13] - a[j + 15];
-        a[j + 8] = x0r + x2r;
-        a[j + 9] = x0i + x2i;
-        x0r -= x2r;
-        x0i -= x2i;
-        a[j + 12] = -wk2i * x0r - wk2r * x0i;
-        a[j + 13] = -wk2i * x0i + wk2r * x0r;
-        x0r = x1r - x3i;
-        x0i = x1i + x3r;
-        a[j + 10] = wk1r * x0r - wk1i * x0i;
-        a[j + 11] = wk1r * x0i + wk1i * x0r;
-        x0r = x1r + x3i;
-        x0i = x1i - x3r;
-        a[j + 14] = wk3r * x0r - wk3i * x0i;
-        a[j + 15] = wk3r * x0i + wk3i * x0r;
-    }
-}
-
-
-static void cftmdl(size_t n, size_t l, float *a, float *w)
-{
-    size_t j, j1, j2, j3, k, k1, k2, m, m2;
-    float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
-    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
-
-    m = l << 2;
-    for (j = 0; j < l; j += 2) {
-        j1 = j + l;
-        j2 = j1 + l;
-        j3 = j2 + l;
-        x0r = a[j] + a[j1];
-        x0i = a[j + 1] + a[j1 + 1];
-        x1r = a[j] - a[j1];
-        x1i = a[j + 1] - a[j1 + 1];
-        x2r = a[j2] + a[j3];
-        x2i = a[j2 + 1] + a[j3 + 1];
-        x3r = a[j2] - a[j3];
-        x3i = a[j2 + 1] - a[j3 + 1];
-        a[j] = x0r + x2r;
-        a[j + 1] = x0i + x2i;
-        a[j2] = x0r - x2r;
-        a[j2 + 1] = x0i - x2i;
-        a[j1] = x1r - x3i;
-        a[j1 + 1] = x1i + x3r;
-        a[j3] = x1r + x3i;
-        a[j3 + 1] = x1i - x3r;
-    }
-    wk1r = w[2];
-    for (j = m; j < l + m; j += 2) {
-        j1 = j + l;
-        j2 = j1 + l;
-        j3 = j2 + l;
-        x0r = a[j] + a[j1];
-        x0i = a[j + 1] + a[j1 + 1];
-        x1r = a[j] - a[j1];
-        x1i = a[j + 1] - a[j1 + 1];
-        x2r = a[j2] + a[j3];
-        x2i = a[j2 + 1] + a[j3 + 1];
-        x3r = a[j2] - a[j3];
-        x3i = a[j2 + 1] - a[j3 + 1];
-        a[j] = x0r + x2r;
-        a[j + 1] = x0i + x2i;
-        a[j2] = x2i - x0i;
-        a[j2 + 1] = x0r - x2r;
-        x0r = x1r - x3i;
-        x0i = x1i + x3r;
-        a[j1] = wk1r * (x0r - x0i);
-        a[j1 + 1] = wk1r * (x0r + x0i);
-        x0r = x3i + x1r;
-        x0i = x3r - x1i;
-        a[j3] = wk1r * (x0i - x0r);
-        a[j3 + 1] = wk1r * (x0i + x0r);
-    }
-    k1 = 0;
-    m2 = 2 * m;
-    for (k = m2; k < n; k += m2) {
-        k1 += 2;
-        k2 = 2 * k1;
-        wk2r = w[k1];
-        wk2i = w[k1 + 1];
-        wk1r = w[k2];
-        wk1i = w[k2 + 1];
-        wk3r = wk1r - 2 * wk2i * wk1i;
-        wk3i = 2 * wk2i * wk1r - wk1i;
-        for (j = k; j < l + k; j += 2) {
-            j1 = j + l;
-            j2 = j1 + l;
-            j3 = j2 + l;
-            x0r = a[j] + a[j1];
-            x0i = a[j + 1] + a[j1 + 1];
-            x1r = a[j] - a[j1];
-            x1i = a[j + 1] - a[j1 + 1];
-            x2r = a[j2] + a[j3];
-            x2i = a[j2 + 1] + a[j3 + 1];
-            x3r = a[j2] - a[j3];
-            x3i = a[j2 + 1] - a[j3 + 1];
-            a[j] = x0r + x2r;
-            a[j + 1] = x0i + x2i;
-            x0r -= x2r;
-            x0i -= x2i;
-            a[j2] = wk2r * x0r - wk2i * x0i;
-            a[j2 + 1] = wk2r * x0i + wk2i * x0r;
-            x0r = x1r - x3i;
-            x0i = x1i + x3r;
-            a[j1] = wk1r * x0r - wk1i * x0i;
-            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
-            x0r = x1r + x3i;
-            x0i = x1i - x3r;
-            a[j3] = wk3r * x0r - wk3i * x0i;
-            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
-        }
-        wk1r = w[k2 + 2];
-        wk1i = w[k2 + 3];
-        wk3r = wk1r - 2 * wk2r * wk1i;
-        wk3i = 2 * wk2r * wk1r - wk1i;
-        for (j = k + m; j < l + (k + m); j += 2) {
-            j1 = j + l;
-            j2 = j1 + l;
-            j3 = j2 + l;
-            x0r = a[j] + a[j1];
-            x0i = a[j + 1] + a[j1 + 1];
-            x1r = a[j] - a[j1];
-            x1i = a[j + 1] - a[j1 + 1];
-            x2r = a[j2] + a[j3];
-            x2i = a[j2 + 1] + a[j3 + 1];
-            x3r = a[j2] - a[j3];
-            x3i = a[j2 + 1] - a[j3 + 1];
-            a[j] = x0r + x2r;
-            a[j + 1] = x0i + x2i;
-            x0r -= x2r;
-            x0i -= x2i;
-            a[j2] = -wk2i * x0r - wk2r * x0i;
-            a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
-            x0r = x1r - x3i;
-            x0i = x1i + x3r;
-            a[j1] = wk1r * x0r - wk1i * x0i;
-            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
-            x0r = x1r + x3i;
-            x0i = x1i - x3r;
-            a[j3] = wk3r * x0r - wk3i * x0i;
-            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
-        }
-    }
-}
-
-
-static void rftfsub(size_t n, float *a, size_t nc, float *c)
-{
-    size_t j, k, kk, ks, m;
-    float wkr, wki, xr, xi, yr, yi;
-
-    m = n >> 1;
-    ks = 2 * nc / m;
-    kk = 0;
-    for (j = 2; j < m; j += 2) {
-        k = n - j;
-        kk += ks;
-        wkr = 0.5f - c[nc - kk];
-        wki = c[kk];
-        xr = a[j] - a[k];
-        xi = a[j + 1] + a[k + 1];
-        yr = wkr * xr - wki * xi;
-        yi = wkr * xi + wki * xr;
-        a[j] -= yr;
-        a[j + 1] -= yi;
-        a[k] += yr;
-        a[k + 1] -= yi;
-    }
-}
-
-
-static void rftbsub(size_t n, float *a, size_t nc, float *c)
-{
-    size_t j, k, kk, ks, m;
-    float wkr, wki, xr, xi, yr, yi;
-
-    a[1] = -a[1];
-    m = n >> 1;
-    ks = 2 * nc / m;
-    kk = 0;
-    for (j = 2; j < m; j += 2) {
-        k = n - j;
-        kk += ks;
-        wkr = 0.5f - c[nc - kk];
-        wki = c[kk];
-        xr = a[j] - a[k];
-        xi = a[j + 1] + a[k + 1];
-        yr = wkr * xr + wki * xi;
-        yi = wkr * xi - wki * xr;
-        a[j] -= yr;
-        a[j + 1] = yi - a[j + 1];
-        a[k] += yr;
-        a[k + 1] = yi - a[k + 1];
-    }
-    a[m + 1] = -a[m + 1];
-}
-
-#if 0  // Not used.
-static void dctsub(int n, float *a, int nc, float *c)
-{
-    int j, k, kk, ks, m;
-    float wkr, wki, xr;
-
-    m = n >> 1;
-    ks = nc / n;
-    kk = 0;
-    for (j = 1; j < m; j++) {
-        k = n - j;
-        kk += ks;
-        wkr = c[kk] - c[nc - kk];
-        wki = c[kk] + c[nc - kk];
-        xr = wki * a[j] - wkr * a[k];
-        a[j] = wkr * a[j] + wki * a[k];
-        a[k] = xr;
-    }
-    a[m] *= c[0];
-}
-
-
-static void dstsub(int n, float *a, int nc, float *c)
-{
-    int j, k, kk, ks, m;
-    float wkr, wki, xr;
-
-    m = n >> 1;
-    ks = nc / n;
-    kk = 0;
-    for (j = 1; j < m; j++) {
-        k = n - j;
-        kk += ks;
-        wkr = c[kk] - c[nc - kk];
-        wki = c[kk] + c[nc - kk];
-        xr = wki * a[k] - wkr * a[j];
-        a[k] = wkr * a[k] + wki * a[j];
-        a[j] = xr;
-    }
-    a[m] *= c[0];
-}
-#endif  // Not used.
diff --git a/common_audio/third_party/fft4g/fft4g.cc b/common_audio/third_party/fft4g/fft4g.cc
new file mode 100644
index 0000000000..fadd1bef0a
--- /dev/null
+++ b/common_audio/third_party/fft4g/fft4g.cc
@@ -0,0 +1,864 @@
+/*
+ * http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
+ * 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.
+ *
+ * Changes:
+ * Trivial type modifications by the WebRTC authors.
+ */
+
+/*
+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, float *, int *, float *);
+    void rdft(size_t, int, float *, size_t *, float *);
+    void ddct(int, int, float *, int *, float *);
+    void ddst(int, int, float *, int *, float *);
+    void dfct(int, float *, float *, int *, float *);
+    void dfst(int, float *, float *, int *, float *);
+
+
+-------- 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 (float *)
+                        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 (float *)
+                        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 (size_t)
+                        n >= 2, n = power of 2
+        a[0...n-1]     :input/output data (float *)
+                        <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 (size_t *)
+                        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 (float *)
+                        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 (float *)
+                        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 (float *)
+                        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 (float *)
+                        <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 (float *)
+                        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 (float *)
+                        output data
+                            a[k] = C[k], 0<=k<=n
+        t[0...n/2]     :work area (float *)
+        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 (float *)
+                        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 (float *)
+                        output data
+                            a[k] = S[k], 0<k<n
+                        (a[0] is used for work area)
+        t[0...n/2-1]   :work area (float *)
+        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 (float *)
+                        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.
+*/
+
+#include <math.h>
+#include <stddef.h>
+
+namespace webrtc {
+
+namespace {
+
+void makewt(size_t nw, size_t* ip, float* w);
+void makect(size_t nc, size_t* ip, float* c);
+void bitrv2(size_t n, size_t* ip, float* a);
+void cftfsub(size_t n, float* a, float* w);
+void cftbsub(size_t n, float* a, float* w);
+void cft1st(size_t n, float* a, float* w);
+void cftmdl(size_t n, size_t l, float* a, float* w);
+void rftfsub(size_t n, float* a, size_t nc, float* c);
+void rftbsub(size_t n, float* a, size_t nc, float* c);
+
+/* -------- initializing routines -------- */
+
+void makewt(size_t nw, size_t* ip, float* w) {
+  size_t j, nwh;
+  float delta, x, y;
+
+  ip[0] = nw;
+  ip[1] = 1;
+  if (nw > 2) {
+    nwh = nw >> 1;
+    delta = atanf(1.0f) / nwh;
+    w[0] = 1;
+    w[1] = 0;
+    w[nwh] = (float)cos(delta * nwh);
+    w[nwh + 1] = w[nwh];
+    if (nwh > 2) {
+      for (j = 2; j < nwh; j += 2) {
+        x = (float)cos(delta * j);
+        y = (float)sin(delta * j);
+        w[j] = x;
+        w[j + 1] = y;
+        w[nw - j] = y;
+        w[nw - j + 1] = x;
+      }
+      bitrv2(nw, ip + 2, w);
+    }
+  }
+}
+
+void makect(size_t nc, size_t* ip, float* c) {
+  size_t j, nch;
+  float delta;
+
+  ip[1] = nc;
+  if (nc > 1) {
+    nch = nc >> 1;
+    delta = atanf(1.0f) / nch;
+    c[0] = (float)cos(delta * nch);
+    c[nch] = 0.5f * c[0];
+    for (j = 1; j < nch; j++) {
+      c[j] = 0.5f * (float)cos(delta * j);
+      c[nc - j] = 0.5f * (float)sin(delta * j);
+    }
+  }
+}
+
+/* -------- child routines -------- */
+
+void bitrv2(size_t n, size_t* ip, float* a) {
+  size_t j, j1, k, k1, l, m, m2;
+  float xr, xi, yr, yi;
+
+  ip[0] = 0;
+  l = n;
+  m = 1;
+  while ((m << 3) < l) {
+    l >>= 1;
+    for (j = 0; j < m; j++) {
+      ip[m + j] = ip[j] + l;
+    }
+    m <<= 1;
+  }
+  m2 = 2 * m;
+  if ((m << 3) == l) {
+    for (k = 0; k < m; k++) {
+      for (j = 0; j < k; j++) {
+        j1 = 2 * j + ip[k];
+        k1 = 2 * k + ip[j];
+        xr = a[j1];
+        xi = a[j1 + 1];
+        yr = a[k1];
+        yi = a[k1 + 1];
+        a[j1] = yr;
+        a[j1 + 1] = yi;
+        a[k1] = xr;
+        a[k1 + 1] = xi;
+        j1 += m2;
+        k1 += 2 * m2;
+        xr = a[j1];
+        xi = a[j1 + 1];
+        yr = a[k1];
+        yi = a[k1 + 1];
+        a[j1] = yr;
+        a[j1 + 1] = yi;
+        a[k1] = xr;
+        a[k1 + 1] = xi;
+        j1 += m2;
+        k1 -= m2;
+        xr = a[j1];
+        xi = a[j1 + 1];
+        yr = a[k1];
+        yi = a[k1 + 1];
+        a[j1] = yr;
+        a[j1 + 1] = yi;
+        a[k1] = xr;
+        a[k1 + 1] = xi;
+        j1 += m2;
+        k1 += 2 * m2;
+        xr = a[j1];
+        xi = a[j1 + 1];
+        yr = a[k1];
+        yi = a[k1 + 1];
+        a[j1] = yr;
+        a[j1 + 1] = yi;
+        a[k1] = xr;
+        a[k1 + 1] = xi;
+      }
+      j1 = 2 * k + m2 + ip[k];
+      k1 = j1 + m2;
+      xr = a[j1];
+      xi = a[j1 + 1];
+      yr = a[k1];
+      yi = a[k1 + 1];
+      a[j1] = yr;
+      a[j1 + 1] = yi;
+      a[k1] = xr;
+      a[k1 + 1] = xi;
+    }
+  } else {
+    for (k = 1; k < m; k++) {
+      for (j = 0; j < k; j++) {
+        j1 = 2 * j + ip[k];
+        k1 = 2 * k + ip[j];
+        xr = a[j1];
+        xi = a[j1 + 1];
+        yr = a[k1];
+        yi = a[k1 + 1];
+        a[j1] = yr;
+        a[j1 + 1] = yi;
+        a[k1] = xr;
+        a[k1 + 1] = xi;
+        j1 += m2;
+        k1 += m2;
+        xr = a[j1];
+        xi = a[j1 + 1];
+        yr = a[k1];
+        yi = a[k1 + 1];
+        a[j1] = yr;
+        a[j1 + 1] = yi;
+        a[k1] = xr;
+        a[k1 + 1] = xi;
+      }
+    }
+  }
+}
+
+void cftfsub(size_t n, float* a, float* w) {
+  size_t j, j1, j2, j3, l;
+  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+  l = 2;
+  if (n > 8) {
+    cft1st(n, a, w);
+    l = 8;
+    while ((l << 2) < n) {
+      cftmdl(n, l, a, w);
+      l <<= 2;
+    }
+  }
+  if ((l << 2) == n) {
+    for (j = 0; j < l; j += 2) {
+      j1 = j + l;
+      j2 = j1 + l;
+      j3 = j2 + l;
+      x0r = a[j] + a[j1];
+      x0i = a[j + 1] + a[j1 + 1];
+      x1r = a[j] - a[j1];
+      x1i = a[j + 1] - a[j1 + 1];
+      x2r = a[j2] + a[j3];
+      x2i = a[j2 + 1] + a[j3 + 1];
+      x3r = a[j2] - a[j3];
+      x3i = a[j2 + 1] - a[j3 + 1];
+      a[j] = x0r + x2r;
+      a[j + 1] = x0i + x2i;
+      a[j2] = x0r - x2r;
+      a[j2 + 1] = x0i - x2i;
+      a[j1] = x1r - x3i;
+      a[j1 + 1] = x1i + x3r;
+      a[j3] = x1r + x3i;
+      a[j3 + 1] = x1i - x3r;
+    }
+  } else {
+    for (j = 0; j < l; j += 2) {
+      j1 = j + l;
+      x0r = a[j] - a[j1];
+      x0i = a[j + 1] - a[j1 + 1];
+      a[j] += a[j1];
+      a[j + 1] += a[j1 + 1];
+      a[j1] = x0r;
+      a[j1 + 1] = x0i;
+    }
+  }
+}
+
+void cftbsub(size_t n, float* a, float* w) {
+  size_t j, j1, j2, j3, l;
+  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+  l = 2;
+  if (n > 8) {
+    cft1st(n, a, w);
+    l = 8;
+    while ((l << 2) < n) {
+      cftmdl(n, l, a, w);
+      l <<= 2;
+    }
+  }
+  if ((l << 2) == n) {
+    for (j = 0; j < l; j += 2) {
+      j1 = j + l;
+      j2 = j1 + l;
+      j3 = j2 + l;
+      x0r = a[j] + a[j1];
+      x0i = -a[j + 1] - a[j1 + 1];
+      x1r = a[j] - a[j1];
+      x1i = -a[j + 1] + a[j1 + 1];
+      x2r = a[j2] + a[j3];
+      x2i = a[j2 + 1] + a[j3 + 1];
+      x3r = a[j2] - a[j3];
+      x3i = a[j2 + 1] - a[j3 + 1];
+      a[j] = x0r + x2r;
+      a[j + 1] = x0i - x2i;
+      a[j2] = x0r - x2r;
+      a[j2 + 1] = x0i + x2i;
+      a[j1] = x1r - x3i;
+      a[j1 + 1] = x1i - x3r;
+      a[j3] = x1r + x3i;
+      a[j3 + 1] = x1i + x3r;
+    }
+  } else {
+    for (j = 0; j < l; j += 2) {
+      j1 = j + l;
+      x0r = a[j] - a[j1];
+      x0i = -a[j + 1] + a[j1 + 1];
+      a[j] += a[j1];
+      a[j + 1] = -a[j + 1] - a[j1 + 1];
+      a[j1] = x0r;
+      a[j1 + 1] = x0i;
+    }
+  }
+}
+
+void cft1st(size_t n, float* a, float* w) {
+  size_t j, k1, k2;
+  float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
+  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+  x0r = a[0] + a[2];
+  x0i = a[1] + a[3];
+  x1r = a[0] - a[2];
+  x1i = a[1] - a[3];
+  x2r = a[4] + a[6];
+  x2i = a[5] + a[7];
+  x3r = a[4] - a[6];
+  x3i = a[5] - a[7];
+  a[0] = x0r + x2r;
+  a[1] = x0i + x2i;
+  a[4] = x0r - x2r;
+  a[5] = x0i - x2i;
+  a[2] = x1r - x3i;
+  a[3] = x1i + x3r;
+  a[6] = x1r + x3i;
+  a[7] = x1i - x3r;
+  wk1r = w[2];
+  x0r = a[8] + a[10];
+  x0i = a[9] + a[11];
+  x1r = a[8] - a[10];
+  x1i = a[9] - a[11];
+  x2r = a[12] + a[14];
+  x2i = a[13] + a[15];
+  x3r = a[12] - a[14];
+  x3i = a[13] - a[15];
+  a[8] = x0r + x2r;
+  a[9] = x0i + x2i;
+  a[12] = x2i - x0i;
+  a[13] = x0r - x2r;
+  x0r = x1r - x3i;
+  x0i = x1i + x3r;
+  a[10] = wk1r * (x0r - x0i);
+  a[11] = wk1r * (x0r + x0i);
+  x0r = x3i + x1r;
+  x0i = x3r - x1i;
+  a[14] = wk1r * (x0i - x0r);
+  a[15] = wk1r * (x0i + x0r);
+  k1 = 0;
+  for (j = 16; j < n; j += 16) {
+    k1 += 2;
+    k2 = 2 * k1;
+    wk2r = w[k1];
+    wk2i = w[k1 + 1];
+    wk1r = w[k2];
+    wk1i = w[k2 + 1];
+    wk3r = wk1r - 2 * wk2i * wk1i;
+    wk3i = 2 * wk2i * wk1r - wk1i;
+    x0r = a[j] + a[j + 2];
+    x0i = a[j + 1] + a[j + 3];
+    x1r = a[j] - a[j + 2];
+    x1i = a[j + 1] - a[j + 3];
+    x2r = a[j + 4] + a[j + 6];
+    x2i = a[j + 5] + a[j + 7];
+    x3r = a[j + 4] - a[j + 6];
+    x3i = a[j + 5] - a[j + 7];
+    a[j] = x0r + x2r;
+    a[j + 1] = x0i + x2i;
+    x0r -= x2r;
+    x0i -= x2i;
+    a[j + 4] = wk2r * x0r - wk2i * x0i;
+    a[j + 5] = wk2r * x0i + wk2i * x0r;
+    x0r = x1r - x3i;
+    x0i = x1i + x3r;
+    a[j + 2] = wk1r * x0r - wk1i * x0i;
+    a[j + 3] = wk1r * x0i + wk1i * x0r;
+    x0r = x1r + x3i;
+    x0i = x1i - x3r;
+    a[j + 6] = wk3r * x0r - wk3i * x0i;
+    a[j + 7] = wk3r * x0i + wk3i * x0r;
+    wk1r = w[k2 + 2];
+    wk1i = w[k2 + 3];
+    wk3r = wk1r - 2 * wk2r * wk1i;
+    wk3i = 2 * wk2r * wk1r - wk1i;
+    x0r = a[j + 8] + a[j + 10];
+    x0i = a[j + 9] + a[j + 11];
+    x1r = a[j + 8] - a[j + 10];
+    x1i = a[j + 9] - a[j + 11];
+    x2r = a[j + 12] + a[j + 14];
+    x2i = a[j + 13] + a[j + 15];
+    x3r = a[j + 12] - a[j + 14];
+    x3i = a[j + 13] - a[j + 15];
+    a[j + 8] = x0r + x2r;
+    a[j + 9] = x0i + x2i;
+    x0r -= x2r;
+    x0i -= x2i;
+    a[j + 12] = -wk2i * x0r - wk2r * x0i;
+    a[j + 13] = -wk2i * x0i + wk2r * x0r;
+    x0r = x1r - x3i;
+    x0i = x1i + x3r;
+    a[j + 10] = wk1r * x0r - wk1i * x0i;
+    a[j + 11] = wk1r * x0i + wk1i * x0r;
+    x0r = x1r + x3i;
+    x0i = x1i - x3r;
+    a[j + 14] = wk3r * x0r - wk3i * x0i;
+    a[j + 15] = wk3r * x0i + wk3i * x0r;
+  }
+}
+
+void cftmdl(size_t n, size_t l, float* a, float* w) {
+  size_t j, j1, j2, j3, k, k1, k2, m, m2;
+  float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
+  float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
+
+  m = l << 2;
+  for (j = 0; j < l; j += 2) {
+    j1 = j + l;
+    j2 = j1 + l;
+    j3 = j2 + l;
+    x0r = a[j] + a[j1];
+    x0i = a[j + 1] + a[j1 + 1];
+    x1r = a[j] - a[j1];
+    x1i = a[j + 1] - a[j1 + 1];
+    x2r = a[j2] + a[j3];
+    x2i = a[j2 + 1] + a[j3 + 1];
+    x3r = a[j2] - a[j3];
+    x3i = a[j2 + 1] - a[j3 + 1];
+    a[j] = x0r + x2r;
+    a[j + 1] = x0i + x2i;
+    a[j2] = x0r - x2r;
+    a[j2 + 1] = x0i - x2i;
+    a[j1] = x1r - x3i;
+    a[j1 + 1] = x1i + x3r;
+    a[j3] = x1r + x3i;
+    a[j3 + 1] = x1i - x3r;
+  }
+  wk1r = w[2];
+  for (j = m; j < l + m; j += 2) {
+    j1 = j + l;
+    j2 = j1 + l;
+    j3 = j2 + l;
+    x0r = a[j] + a[j1];
+    x0i = a[j + 1] + a[j1 + 1];
+    x1r = a[j] - a[j1];
+    x1i = a[j + 1] - a[j1 + 1];
+    x2r = a[j2] + a[j3];
+    x2i = a[j2 + 1] + a[j3 + 1];
+    x3r = a[j2] - a[j3];
+    x3i = a[j2 + 1] - a[j3 + 1];
+    a[j] = x0r + x2r;
+    a[j + 1] = x0i + x2i;
+    a[j2] = x2i - x0i;
+    a[j2 + 1] = x0r - x2r;
+    x0r = x1r - x3i;
+    x0i = x1i + x3r;
+    a[j1] = wk1r * (x0r - x0i);
+    a[j1 + 1] = wk1r * (x0r + x0i);
+    x0r = x3i + x1r;
+    x0i = x3r - x1i;
+    a[j3] = wk1r * (x0i - x0r);
+    a[j3 + 1] = wk1r * (x0i + x0r);
+  }
+  k1 = 0;
+  m2 = 2 * m;
+  for (k = m2; k < n; k += m2) {
+    k1 += 2;
+    k2 = 2 * k1;
+    wk2r = w[k1];
+    wk2i = w[k1 + 1];
+    wk1r = w[k2];
+    wk1i = w[k2 + 1];
+    wk3r = wk1r - 2 * wk2i * wk1i;
+    wk3i = 2 * wk2i * wk1r - wk1i;
+    for (j = k; j < l + k; j += 2) {
+      j1 = j + l;
+      j2 = j1 + l;
+      j3 = j2 + l;
+      x0r = a[j] + a[j1];
+      x0i = a[j + 1] + a[j1 + 1];
+      x1r = a[j] - a[j1];
+      x1i = a[j + 1] - a[j1 + 1];
+      x2r = a[j2] + a[j3];
+      x2i = a[j2 + 1] + a[j3 + 1];
+      x3r = a[j2] - a[j3];
+      x3i = a[j2 + 1] - a[j3 + 1];
+      a[j] = x0r + x2r;
+      a[j + 1] = x0i + x2i;
+      x0r -= x2r;
+      x0i -= x2i;
+      a[j2] = wk2r * x0r - wk2i * x0i;
+      a[j2 + 1] = wk2r * x0i + wk2i * x0r;
+      x0r = x1r - x3i;
+      x0i = x1i + x3r;
+      a[j1] = wk1r * x0r - wk1i * x0i;
+      a[j1 + 1] = wk1r * x0i + wk1i * x0r;
+      x0r = x1r + x3i;
+      x0i = x1i - x3r;
+      a[j3] = wk3r * x0r - wk3i * x0i;
+      a[j3 + 1] = wk3r * x0i + wk3i * x0r;
+    }
+    wk1r = w[k2 + 2];
+    wk1i = w[k2 + 3];
+    wk3r = wk1r - 2 * wk2r * wk1i;
+    wk3i = 2 * wk2r * wk1r - wk1i;
+    for (j = k + m; j < l + (k + m); j += 2) {
+      j1 = j + l;
+      j2 = j1 + l;
+      j3 = j2 + l;
+      x0r = a[j] + a[j1];
+      x0i = a[j + 1] + a[j1 + 1];
+      x1r = a[j] - a[j1];
+      x1i = a[j + 1] - a[j1 + 1];
+      x2r = a[j2] + a[j3];
+      x2i = a[j2 + 1] + a[j3 + 1];
+      x3r = a[j2] - a[j3];
+      x3i = a[j2 + 1] - a[j3 + 1];
+      a[j] = x0r + x2r;
+      a[j + 1] = x0i + x2i;
+      x0r -= x2r;
+      x0i -= x2i;
+      a[j2] = -wk2i * x0r - wk2r * x0i;
+      a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
+      x0r = x1r - x3i;
+      x0i = x1i + x3r;
+      a[j1] = wk1r * x0r - wk1i * x0i;
+      a[j1 + 1] = wk1r * x0i + wk1i * x0r;
+      x0r = x1r + x3i;
+      x0i = x1i - x3r;
+      a[j3] = wk3r * x0r - wk3i * x0i;
+      a[j3 + 1] = wk3r * x0i + wk3i * x0r;
+    }
+  }
+}
+
+void rftfsub(size_t n, float* a, size_t nc, float* c) {
+  size_t j, k, kk, ks, m;
+  float wkr, wki, xr, xi, yr, yi;
+
+  m = n >> 1;
+  ks = 2 * nc / m;
+  kk = 0;
+  for (j = 2; j < m; j += 2) {
+    k = n - j;
+    kk += ks;
+    wkr = 0.5f - c[nc - kk];
+    wki = c[kk];
+    xr = a[j] - a[k];
+    xi = a[j + 1] + a[k + 1];
+    yr = wkr * xr - wki * xi;
+    yi = wkr * xi + wki * xr;
+    a[j] -= yr;
+    a[j + 1] -= yi;
+    a[k] += yr;
+    a[k + 1] -= yi;
+  }
+}
+
+void rftbsub(size_t n, float* a, size_t nc, float* c) {
+  size_t j, k, kk, ks, m;
+  float wkr, wki, xr, xi, yr, yi;
+
+  a[1] = -a[1];
+  m = n >> 1;
+  ks = 2 * nc / m;
+  kk = 0;
+  for (j = 2; j < m; j += 2) {
+    k = n - j;
+    kk += ks;
+    wkr = 0.5f - c[nc - kk];
+    wki = c[kk];
+    xr = a[j] - a[k];
+    xi = a[j + 1] + a[k + 1];
+    yr = wkr * xr + wki * xi;
+    yi = wkr * xi - wki * xr;
+    a[j] -= yr;
+    a[j + 1] = yi - a[j + 1];
+    a[k] += yr;
+    a[k + 1] = yi - a[k + 1];
+  }
+  a[m + 1] = -a[m + 1];
+}
+
+}  // namespace
+
+void WebRtc_rdft(size_t n, int isgn, float* a, size_t* ip, float* w) {
+  size_t nw, nc;
+  float xi;
+
+  nw = ip[0];
+  if (n > (nw << 2)) {
+    nw = n >> 2;
+    makewt(nw, ip, w);
+  }
+  nc = ip[1];
+  if (n > (nc << 2)) {
+    nc = n >> 2;
+    makect(nc, ip, w + nw);
+  }
+  if (isgn >= 0) {
+    if (n > 4) {
+      bitrv2(n, ip + 2, a);
+      cftfsub(n, a, w);
+      rftfsub(n, a, nc, w + nw);
+    } else if (n == 4) {
+      cftfsub(n, a, w);
+    }
+    xi = a[0] - a[1];
+    a[0] += a[1];
+    a[1] = xi;
+  } else {
+    a[1] = 0.5f * (a[0] - a[1]);
+    a[0] -= a[1];
+    if (n > 4) {
+      rftbsub(n, a, nc, w + nw);
+      bitrv2(n, ip + 2, a);
+      cftbsub(n, a, w);
+    } else if (n == 4) {
+      cftfsub(n, a, w);
+    }
+  }
+}
+
+}  // namespace webrtc
diff --git a/common_audio/third_party/fft4g/fft4g.h b/common_audio/third_party/fft4g/fft4g.h
index 0820b6e908..7cdc695633 100644
--- a/common_audio/third_party/fft4g/fft4g.h
+++ b/common_audio/third_party/fft4g/fft4g.h
@@ -11,15 +11,11 @@
 #ifndef COMMON_AUDIO_THIRD_PARTY_FFT4G_FFT4G_H_
 #define COMMON_AUDIO_THIRD_PARTY_FFT4G_FFT4G_H_
 
-#if defined(__cplusplus)
-extern "C" {
-#endif
+namespace webrtc {
 
 // Refer to fft4g.c for documentation.
 void WebRtc_rdft(size_t n, int isgn, float* a, size_t* ip, float* w);
 
-#if defined(__cplusplus)
-}
-#endif
+}  // namespace webrtc
 
 #endif /* COMMON_AUDIO_THIRD_PARTY_FFT4G_FFT4G_H_ */