libavutil: add an FFT & MDCT implementation

This commit adds a new API to libavutil to allow for arbitrary transformations
on various types of data.
This is a partly new implementation, with the power of two transforms taken
from libavcodec/fft_template, the 5 and 15-point FFT taken from mdct15, while
the 3-point FFT was written from scratch.
The (i)mdct folding code is taken from mdct15 as well, as the mdct_template
code was somewhat old, messy and not easy to separate.

A notable feature of this implementation is that it allows for 3xM and 5xM
based transforms, where M is a power of two, e.g. 384, 640, 768, 1280, etc.
AC-4 uses 3xM transforms while Siren uses 5xM transforms, so the code will
allow for decoding of such streams.
A non-exaustive list of supported sizes:
4, 8, 12, 16, 20, 24, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240,
256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560...

The API was designed such that it allows for not only 1D transforms but also
2D transforms of certain block sizes. This was partly on accident as the stride
argument is required for Opus MDCTs, but can be used in the context of a 2D
transform as well.
Also, various data types would be implemented eventually as well, such as
"double" and "int32_t".

Some performance comparisons with libfftw3f (SIMD disabled for both):
120:
  22353 decicycles in     fftwf_execute,     1024 runs,      0 skips
  21836 decicycles in compound_fft_15x8,     1024 runs,      0 skips

128:
  22003 decicycles in       fftwf_execute,   1024 runs,      0 skips
  23132 decicycles in monolithic_fft_ptwo,   1024 runs,      0 skips

384:
  75939 decicycles in      fftwf_execute,    1024 runs,      0 skips
  73973 decicycles in compound_fft_3x128,    1024 runs,      0 skips

640:
 104354 decicycles in       fftwf_execute,   1024 runs,      0 skips
 149518 decicycles in compound_fft_5x128,    1024 runs,      0 skips

768:
 109323 decicycles in      fftwf_execute,    1024 runs,      0 skips
 164096 decicycles in compound_fft_3x256,    1024 runs,      0 skips

960:
 186210 decicycles in      fftwf_execute,    1024 runs,      0 skips
 215256 decicycles in compound_fft_15x64,    1024 runs,      0 skips

1024:
 163464 decicycles in       fftwf_execute,   1024 runs,      0 skips
 199686 decicycles in monolithic_fft_ptwo,   1024 runs,      0 skips

With SIMD we should be faster than fftw for 15xM transforms as our fft15 SIMD
is around 2x faster than theirs, even if our ptwo SIMD is slightly slower.

The goal is to remove the libavcodec/mdct15 code and deprecate the
libavcodec/avfft interface once aarch64 and x86 SIMD code has been ported.
New code throughout the project should use this API.

The implementation passes fate when used in Opus, AAC and Vorbis, and the output
is identical with ATRAC9 as well.

1 files changed, 803 insertions, 0 deletions

diff --git a/libavutil/tx.c b/libavutil/tx.c
new file mode 100644
index 0000000..934ef27
--- /dev/null
+++ b/libavutil/tx.c
@@ -0,0 +1,803 @@
+/*
+ * Copyright (c) 2019 Lynne <dev@lynne.ee>
+ * Power of two FFT:
+ * Copyright (c) 2008 Loren Merritt
+ * Copyright (c) 2002 Fabrice Bellard
+ * Partly based on libdjbfft by D. J. Bernstein
+ *
+ * This file is part of FFmpeg.
+ *
+ * FFmpeg 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.
+ *
+ * FFmpeg 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 FFmpeg; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+
+#include <stddef.h>
+#include "tx.h"
+#include "thread.h"
+#include "mem.h"
+#include "avassert.h"
+
+typedef float FFTSample;
+typedef AVComplexFloat FFTComplex;
+
+struct AVTXContext {
+    int n;              /* Nptwo part */
+    int m;              /* Ptwo part */
+
+    FFTComplex *exptab; /* MDCT exptab */
+    FFTComplex *tmp;    /* Temporary buffer needed for all compound transforms */
+    int        *pfatab; /* Input/Output mapping for compound transforms */
+    int        *revtab; /* Input mapping for power of two transforms */
+};
+
+#define FFT_NAME(x) x
+
+#define COSTABLE(size) \
+    static DECLARE_ALIGNED(32, FFTSample, FFT_NAME(ff_cos_##size))[size/2]
+
+static FFTSample * const FFT_NAME(ff_cos_tabs)[18];
+
+COSTABLE(16);
+COSTABLE(32);
+COSTABLE(64);
+COSTABLE(128);
+COSTABLE(256);
+COSTABLE(512);
+COSTABLE(1024);
+COSTABLE(2048);
+COSTABLE(4096);
+COSTABLE(8192);
+COSTABLE(16384);
+COSTABLE(32768);
+COSTABLE(65536);
+COSTABLE(131072);
+
+static av_cold void init_ff_cos_tabs(int index)
+{
+    int m = 1 << index;
+    double freq = 2*M_PI/m;
+    FFTSample *tab = FFT_NAME(ff_cos_tabs)[index];
+    for(int i = 0; i <= m/4; i++)
+        tab[i] = cos(i*freq);
+    for(int i = 1; i < m/4; i++)
+        tab[m/2 - i] = tab[i];
+}
+
+typedef struct CosTabsInitOnce {
+    void (*func)(void);
+    AVOnce control;
+} CosTabsInitOnce;
+
+#define INIT_FF_COS_TABS_FUNC(index, size)                                     \
+static av_cold void init_ff_cos_tabs_ ## size (void)                           \
+{                                                                              \
+    init_ff_cos_tabs(index);                                                   \
+}
+
+INIT_FF_COS_TABS_FUNC(4, 16)
+INIT_FF_COS_TABS_FUNC(5, 32)
+INIT_FF_COS_TABS_FUNC(6, 64)
+INIT_FF_COS_TABS_FUNC(7, 128)
+INIT_FF_COS_TABS_FUNC(8, 256)
+INIT_FF_COS_TABS_FUNC(9, 512)
+INIT_FF_COS_TABS_FUNC(10, 1024)
+INIT_FF_COS_TABS_FUNC(11, 2048)
+INIT_FF_COS_TABS_FUNC(12, 4096)
+INIT_FF_COS_TABS_FUNC(13, 8192)
+INIT_FF_COS_TABS_FUNC(14, 16384)
+INIT_FF_COS_TABS_FUNC(15, 32768)
+INIT_FF_COS_TABS_FUNC(16, 65536)
+INIT_FF_COS_TABS_FUNC(17, 131072)
+
+static CosTabsInitOnce cos_tabs_init_once[] = {
+    { NULL },
+    { NULL },
+    { NULL },
+    { NULL },
+    { init_ff_cos_tabs_16, AV_ONCE_INIT },
+    { init_ff_cos_tabs_32, AV_ONCE_INIT },
+    { init_ff_cos_tabs_64, AV_ONCE_INIT },
+    { init_ff_cos_tabs_128, AV_ONCE_INIT },
+    { init_ff_cos_tabs_256, AV_ONCE_INIT },
+    { init_ff_cos_tabs_512, AV_ONCE_INIT },
+    { init_ff_cos_tabs_1024, AV_ONCE_INIT },
+    { init_ff_cos_tabs_2048, AV_ONCE_INIT },
+    { init_ff_cos_tabs_4096, AV_ONCE_INIT },
+    { init_ff_cos_tabs_8192, AV_ONCE_INIT },
+    { init_ff_cos_tabs_16384, AV_ONCE_INIT },
+    { init_ff_cos_tabs_32768, AV_ONCE_INIT },
+    { init_ff_cos_tabs_65536, AV_ONCE_INIT },
+    { init_ff_cos_tabs_131072, AV_ONCE_INIT },
+};
+
+static FFTSample * const FFT_NAME(ff_cos_tabs)[] = {
+    NULL, NULL, NULL, NULL,
+    FFT_NAME(ff_cos_16),
+    FFT_NAME(ff_cos_32),
+    FFT_NAME(ff_cos_64),
+    FFT_NAME(ff_cos_128),
+    FFT_NAME(ff_cos_256),
+    FFT_NAME(ff_cos_512),
+    FFT_NAME(ff_cos_1024),
+    FFT_NAME(ff_cos_2048),
+    FFT_NAME(ff_cos_4096),
+    FFT_NAME(ff_cos_8192),
+    FFT_NAME(ff_cos_16384),
+    FFT_NAME(ff_cos_32768),
+    FFT_NAME(ff_cos_65536),
+    FFT_NAME(ff_cos_131072),
+};
+
+static av_cold void ff_init_ff_cos_tabs(int index)
+{
+    ff_thread_once(&cos_tabs_init_once[index].control,
+                    cos_tabs_init_once[index].func);
+}
+
+static AVOnce tabs_53_once = AV_ONCE_INIT;
+static DECLARE_ALIGNED(32, FFTComplex, FFT_NAME(ff_53_tabs))[4];
+
+static av_cold void ff_init_53_tabs(void)
+{
+    ff_53_tabs[0] = (FFTComplex){ cos(2 * M_PI / 12), cos(2 * M_PI / 12) };
+    ff_53_tabs[1] = (FFTComplex){ 0.5, 0.5 };
+    ff_53_tabs[2] = (FFTComplex){ cos(2 * M_PI /  5), sin(2 * M_PI /  5) };
+    ff_53_tabs[3] = (FFTComplex){ cos(2 * M_PI / 10), sin(2 * M_PI / 10) };
+}
+
+#define BF(x, y, a, b) do {                                                    \
+        x = (a) - (b);                                                         \
+        y = (a) + (b);                                                         \
+    } while (0)
+
+#define CMUL(dre, dim, are, aim, bre, bim) do {                                \
+        (dre) = (are) * (bre) - (aim) * (bim);                                 \
+        (dim) = (are) * (bim) + (aim) * (bre);                                 \
+    } while (0)
+
+#define CMUL3(c, a, b) CMUL((c).re, (c).im, (a).re, (a).im, (b).re, (b).im)
+
+static av_always_inline void fft3(FFTComplex *out, FFTComplex *in,
+                                  ptrdiff_t stride)
+{
+    FFTComplex tmp[2];
+
+    tmp[0].re = in[1].im - in[2].im;
+    tmp[0].im = in[1].re - in[2].re;
+    tmp[1].re = in[1].re + in[2].re;
+    tmp[1].im = in[1].im + in[2].im;
+
+    out[0*stride].re = in[0].re + tmp[1].re;
+    out[0*stride].im = in[0].im + tmp[1].im;
+
+    tmp[0].re *= ff_53_tabs[0].re;
+    tmp[0].im *= ff_53_tabs[0].im;
+    tmp[1].re *= ff_53_tabs[1].re;
+    tmp[1].im *= ff_53_tabs[1].re;
+
+    out[1*stride].re = in[0].re - tmp[1].re + tmp[0].re;
+    out[1*stride].im = in[0].im - tmp[1].im - tmp[0].im;
+    out[2*stride].re = in[0].re - tmp[1].re - tmp[0].re;
+    out[2*stride].im = in[0].im - tmp[1].im + tmp[0].im;
+}
+
+#define DECL_FFT5(NAME, D0, D1, D2, D3, D4)                                    \
+static av_always_inline void NAME(FFTComplex *out, FFTComplex *in,             \
+                                  ptrdiff_t stride)                            \
+{                                                                              \
+    FFTComplex z0[4], t[6];                                                    \
+                                                                               \
+    t[0].re = in[1].re + in[4].re;                                             \
+    t[0].im = in[1].im + in[4].im;                                             \
+    t[1].im = in[1].re - in[4].re;                                             \
+    t[1].re = in[1].im - in[4].im;                                             \
+    t[2].re = in[2].re + in[3].re;                                             \
+    t[2].im = in[2].im + in[3].im;                                             \
+    t[3].im = in[2].re - in[3].re;                                             \
+    t[3].re = in[2].im - in[3].im;                                             \
+                                                                               \
+    out[D0*stride].re = in[0].re + in[1].re + in[2].re +                       \
+                        in[3].re + in[4].re;                                   \
+    out[D0*stride].im = in[0].im + in[1].im + in[2].im +                       \
+                        in[3].im + in[4].im;                                   \
+                                                                               \
+    t[4].re = ff_53_tabs[2].re * t[2].re - ff_53_tabs[3].re * t[0].re;         \
+    t[4].im = ff_53_tabs[2].re * t[2].im - ff_53_tabs[3].re * t[0].im;         \
+    t[0].re = ff_53_tabs[2].re * t[0].re - ff_53_tabs[3].re * t[2].re;         \
+    t[0].im = ff_53_tabs[2].re * t[0].im - ff_53_tabs[3].re * t[2].im;         \
+    t[5].re = ff_53_tabs[2].im * t[3].re - ff_53_tabs[3].im * t[1].re;         \
+    t[5].im = ff_53_tabs[2].im * t[3].im - ff_53_tabs[3].im * t[1].im;         \
+    t[1].re = ff_53_tabs[2].im * t[1].re + ff_53_tabs[3].im * t[3].re;         \
+    t[1].im = ff_53_tabs[2].im * t[1].im + ff_53_tabs[3].im * t[3].im;         \
+                                                                               \
+    z0[0].re = t[0].re - t[1].re;                                              \
+    z0[0].im = t[0].im - t[1].im;                                              \
+    z0[1].re = t[4].re + t[5].re;                                              \
+    z0[1].im = t[4].im + t[5].im;                                              \
+                                                                               \
+    z0[2].re = t[4].re - t[5].re;                                              \
+    z0[2].im = t[4].im - t[5].im;                                              \
+    z0[3].re = t[0].re + t[1].re;                                              \
+    z0[3].im = t[0].im + t[1].im;                                              \
+                                                                               \
+    out[D1*stride].re = in[0].re + z0[3].re;                                   \
+    out[D1*stride].im = in[0].im + z0[0].im;                                   \
+    out[D2*stride].re = in[0].re + z0[2].re;                                   \
+    out[D2*stride].im = in[0].im + z0[1].im;                                   \
+    out[D3*stride].re = in[0].re + z0[1].re;                                   \
+    out[D3*stride].im = in[0].im + z0[2].im;                                   \
+    out[D4*stride].re = in[0].re + z0[0].re;                                   \
+    out[D4*stride].im = in[0].im + z0[3].im;                                   \
+}
+
+DECL_FFT5(fft5,     0,  1,  2,  3,  4)
+DECL_FFT5(fft5_m1,  0,  6, 12,  3,  9)
+DECL_FFT5(fft5_m2, 10,  1,  7, 13,  4)
+DECL_FFT5(fft5_m3,  5, 11,  2,  8, 14)
+
+static av_always_inline void fft15(FFTComplex *out, FFTComplex *in,
+                                   ptrdiff_t stride)
+{
+    FFTComplex tmp[15];
+
+    for (int i = 0; i < 5; i++)
+        fft3(tmp + i, in + i*3, 5);
+
+    fft5_m1(out, tmp +  0, stride);
+    fft5_m2(out, tmp +  5, stride);
+    fft5_m3(out, tmp + 10, stride);
+}
+
+#define BUTTERFLIES(a0,a1,a2,a3) {\
+    BF(t3, t5, t5, t1);\
+    BF(a2.re, a0.re, a0.re, t5);\
+    BF(a3.im, a1.im, a1.im, t3);\
+    BF(t4, t6, t2, t6);\
+    BF(a3.re, a1.re, a1.re, t4);\
+    BF(a2.im, a0.im, a0.im, t6);\
+}
+
+// force loading all the inputs before storing any.
+// this is slightly slower for small data, but avoids store->load aliasing
+// for addresses separated by large powers of 2.
+#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
+    FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
+    BF(t3, t5, t5, t1);\
+    BF(a2.re, a0.re, r0, t5);\
+    BF(a3.im, a1.im, i1, t3);\
+    BF(t4, t6, t2, t6);\
+    BF(a3.re, a1.re, r1, t4);\
+    BF(a2.im, a0.im, i0, t6);\
+}
+
+#define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
+    CMUL(t1, t2, a2.re, a2.im, wre, -wim);\
+    CMUL(t5, t6, a3.re, a3.im, wre,  wim);\
+    BUTTERFLIES(a0,a1,a2,a3)\
+}
+
+#define TRANSFORM_ZERO(a0,a1,a2,a3) {\
+    t1 = a2.re;\
+    t2 = a2.im;\
+    t5 = a3.re;\
+    t6 = a3.im;\
+    BUTTERFLIES(a0,a1,a2,a3)\
+}
+
+/* z[0...8n-1], w[1...2n-1] */
+#define PASS(name)\
+static void name(FFTComplex *z, const FFTSample *wre, unsigned int n)\
+{\
+    FFTSample t1, t2, t3, t4, t5, t6;\
+    int o1 = 2*n;\
+    int o2 = 4*n;\
+    int o3 = 6*n;\
+    const FFTSample *wim = wre+o1;\
+    n--;\
+\
+    TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
+    TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
+    do {\
+        z += 2;\
+        wre += 2;\
+        wim -= 2;\
+        TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
+        TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
+    } while(--n);\
+}
+
+PASS(pass)
+#undef BUTTERFLIES
+#define BUTTERFLIES BUTTERFLIES_BIG
+PASS(pass_big)
+
+#define DECL_FFT(n,n2,n4)\
+static void fft##n(FFTComplex *z)\
+{\
+    fft##n2(z);\
+    fft##n4(z+n4*2);\
+    fft##n4(z+n4*3);\
+    pass(z,FFT_NAME(ff_cos_##n),n4/2);\
+}
+
+static void fft4(FFTComplex *z)
+{
+    FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
+
+    BF(t3, t1, z[0].re, z[1].re);
+    BF(t8, t6, z[3].re, z[2].re);
+    BF(z[2].re, z[0].re, t1, t6);
+    BF(t4, t2, z[0].im, z[1].im);
+    BF(t7, t5, z[2].im, z[3].im);
+    BF(z[3].im, z[1].im, t4, t8);
+    BF(z[3].re, z[1].re, t3, t7);
+    BF(z[2].im, z[0].im, t2, t5);
+}
+
+static void fft8(FFTComplex *z)
+{
+    FFTSample t1, t2, t3, t4, t5, t6;
+
+    fft4(z);
+
+    BF(t1, z[5].re, z[4].re, -z[5].re);
+    BF(t2, z[5].im, z[4].im, -z[5].im);
+    BF(t5, z[7].re, z[6].re, -z[7].re);
+    BF(t6, z[7].im, z[6].im, -z[7].im);
+
+    BUTTERFLIES(z[0],z[2],z[4],z[6]);
+    TRANSFORM(z[1],z[3],z[5],z[7],M_SQRT1_2,M_SQRT1_2);
+}
+
+static void fft16(FFTComplex *z)
+{
+    FFTSample t1, t2, t3, t4, t5, t6;
+    FFTSample cos_16_1 = FFT_NAME(ff_cos_16)[1];
+    FFTSample cos_16_3 = FFT_NAME(ff_cos_16)[3];
+
+    fft8(z);
+    fft4(z+8);
+    fft4(z+12);
+
+    TRANSFORM_ZERO(z[0],z[4],z[8],z[12]);
+    TRANSFORM(z[2],z[6],z[10],z[14],M_SQRT1_2,M_SQRT1_2);
+    TRANSFORM(z[1],z[5],z[9],z[13],cos_16_1,cos_16_3);
+    TRANSFORM(z[3],z[7],z[11],z[15],cos_16_3,cos_16_1);
+}
+
+DECL_FFT(32,16,8)
+DECL_FFT(64,32,16)
+DECL_FFT(128,64,32)
+DECL_FFT(256,128,64)
+DECL_FFT(512,256,128)
+#define pass pass_big
+DECL_FFT(1024,512,256)
+DECL_FFT(2048,1024,512)
+DECL_FFT(4096,2048,1024)
+DECL_FFT(8192,4096,2048)
+DECL_FFT(16384,8192,4096)
+DECL_FFT(32768,16384,8192)
+DECL_FFT(65536,32768,16384)
+DECL_FFT(131072,65536,32768)
+
+static void (* const fft_dispatch[])(FFTComplex*) = {
+    fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
+    fft2048, fft4096, fft8192, fft16384, fft32768, fft65536, fft131072
+};
+
+#define DECL_COMP_FFT(N)                                                       \
+static void compound_fft_##N##xM(AVTXContext *s, void *_out,                   \
+                                 void *_in, ptrdiff_t stride)                  \
+{                                                                              \
+    const int m = s->m, *in_map = s->pfatab, *out_map = in_map + N*m;          \
+    FFTComplex *in = _in;                                                      \
+    FFTComplex *out = _out;                                                    \
+    FFTComplex fft##N##in[N];                                                  \
+    void (*fftp)(FFTComplex *z) = fft_dispatch[av_log2(m) - 2];                \
+                                                                               \
+    for (int i = 0; i < m; i++) {                                              \
+        for (int j = 0; j < N; j++)                                            \
+            fft##N##in[j] = in[in_map[i*N + j]];                               \
+        fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
+    }                                                                          \
+                                                                               \
+    for (int i = 0; i < N; i++)                                                \
+        fftp(s->tmp + m*i);                                                    \
+                                                                               \
+    for (int i = 0; i < N*m; i++)                                              \
+        out[i] = s->tmp[out_map[i]];                                           \
+}
+
+DECL_COMP_FFT(3)
+DECL_COMP_FFT(5)
+DECL_COMP_FFT(15)
+
+static void monolithic_fft(AVTXContext *s, void *_out, void *_in,
+                           ptrdiff_t stride)
+{
+    FFTComplex *in = _in;
+    FFTComplex *out = _out;
+    int m = s->m, mb = av_log2(m) - 2;
+    for (int i = 0; i < m; i++)
+        out[s->revtab[i]] = in[i];
+    fft_dispatch[mb](out);
+}
+
+#define DECL_COMP_IMDCT(N)                                                     \
+static void compound_imdct_##N##xM(AVTXContext *s, void *_dst, void *_src,     \
+                                   ptrdiff_t stride)                           \
+{                                                                              \
+    FFTComplex fft##N##in[N];                                                  \
+    FFTComplex *z = _dst, *exp = s->exptab;                                    \
+    const int m = s->m, len8 = N*m >> 1;                                       \
+    const int *in_map = s->pfatab, *out_map = in_map + N*m;                    \
+    const float *src = _src, *in1, *in2;                                       \
+    void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];                 \
+                                                                               \
+    stride /= sizeof(*src); /* To convert it from bytes */                     \
+    in1 = src;                                                                 \
+    in2 = src + ((N*m*2) - 1) * stride;                                        \
+                                                                               \
+    for (int i = 0; i < m; i++) {                                              \
+        for (int j = 0; j < N; j++) {                                          \
+            const int k = in_map[i*N + j];                                     \
+            FFTComplex tmp = { in2[-k*stride], in1[k*stride] };                \
+            CMUL3(fft##N##in[j], tmp, exp[k >> 1]);                            \
+        }                                                                      \
+        fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
+    }                                                                          \
+                                                                               \
+    for (int i = 0; i < N; i++)                                                \
+        fftp(s->tmp + m*i);                                                    \
+                                                                               \
+    for (int i = 0; i < len8; i++) {                                           \
+        const int i0 = len8 + i, i1 = len8 - i - 1;                            \
+        const int s0 = out_map[i0], s1 = out_map[i1];                          \
+        FFTComplex src1 = { s->tmp[s1].im, s->tmp[s1].re };                    \
+        FFTComplex src0 = { s->tmp[s0].im, s->tmp[s0].re };                    \
+                                                                               \
+        CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);    \
+        CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);    \
+    }                                                                          \
+}
+
+DECL_COMP_IMDCT(3)
+DECL_COMP_IMDCT(5)
+DECL_COMP_IMDCT(15)
+
+#define DECL_COMP_MDCT(N)                                                      \
+static void compound_mdct_##N##xM(AVTXContext *s, void *_dst, void *_src,      \
+                                  ptrdiff_t stride)                            \
+{                                                                              \
+    float *src = _src, *dst = _dst;                                            \
+    FFTComplex *exp = s->exptab, tmp, fft##N##in[N];                           \
+    const int m = s->m, len4 = N*m, len3 = len4 * 3, len8 = len4 >> 1;         \
+    const int *in_map = s->pfatab, *out_map = in_map + N*m;                    \
+    void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];                 \
+                                                                               \
+    stride /= sizeof(*dst);                                                    \
+                                                                               \
+    for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */             \
+        for (int j = 0; j < N; j++) {                                          \
+            const int k = in_map[i*N + j];                                     \
+            if (k < len4) {                                                    \
+                tmp.re = -src[ len4 + k] + src[1*len4 - 1 - k];                \
+                tmp.im = -src[ len3 + k] - src[1*len3 - 1 - k];                \
+            } else {                                                           \
+                tmp.re = -src[ len4 + k] - src[5*len4 - 1 - k];                \
+                tmp.im =  src[-len4 + k] - src[1*len3 - 1 - k];                \
+            }                                                                  \
+            CMUL(fft##N##in[j].im, fft##N##in[j].re, tmp.re, tmp.im,           \
+                 exp[k >> 1].re, exp[k >> 1].im);                              \
+        }                                                                      \
+        fft##N(s->tmp + s->revtab[i], fft##N##in, m);                          \
+    }                                                                          \
+                                                                               \
+    for (int i = 0; i < 15; i++)                                               \
+        fftp(s->tmp + m*i);                                                    \
+                                                                               \
+    for (int i = 0; i < len8; i++) {                                           \
+        const int i0 = len8 + i, i1 = len8 - i - 1;                            \
+        const int s0 = out_map[i0], s1 = out_map[i1];                          \
+        FFTComplex src1 = { s->tmp[s1].re, s->tmp[s1].im };                    \
+        FFTComplex src0 = { s->tmp[s0].re, s->tmp[s0].im };                    \
+                                                                               \
+        CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,    \
+             exp[i0].im, exp[i0].re);                                          \
+        CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,    \
+             exp[i1].im, exp[i1].re);                                          \
+    }                                                                          \
+}
+
+DECL_COMP_MDCT(3)
+DECL_COMP_MDCT(5)
+DECL_COMP_MDCT(15)
+
+static void monolithic_imdct(AVTXContext *s, void *_dst, void *_src,
+                             ptrdiff_t stride)
+{
+    FFTComplex *z = _dst, *exp = s->exptab;
+    const int m = s->m, len8 = m >> 1;
+    const float *src = _src, *in1, *in2;
+    void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];
+
+    stride /= sizeof(*src);
+    in1 = src;
+    in2 = src + ((m*2) - 1) * stride;
+
+    for (int i = 0; i < m; i++) {
+        FFTComplex tmp = { in2[-2*i*stride], in1[2*i*stride] };
+        CMUL3(z[s->revtab[i]], tmp, exp[i]);
+    }
+
+    fftp(z);
+
+    for (int i = 0; i < len8; i++) {
+        const int i0 = len8 + i, i1 = len8 - i - 1;
+        FFTComplex src1 = { z[i1].im, z[i1].re };
+        FFTComplex src0 = { z[i0].im, z[i0].re };
+
+        CMUL(z[i1].re, z[i0].im, src1.re, src1.im, exp[i1].im, exp[i1].re);
+        CMUL(z[i0].re, z[i1].im, src0.re, src0.im, exp[i0].im, exp[i0].re);
+    }
+}
+
+static void monolithic_mdct(AVTXContext *s, void *_dst, void *_src,
+                            ptrdiff_t stride)
+{
+    float *src = _src, *dst = _dst;
+    FFTComplex *exp = s->exptab, tmp, *z = _dst;
+    const int m = s->m, len4 = m, len3 = len4 * 3, len8 = len4 >> 1;
+    void (*fftp)(FFTComplex *) = fft_dispatch[av_log2(m) - 2];
+
+    stride /= sizeof(*dst);
+
+    for (int i = 0; i < m; i++) { /* Folding and pre-reindexing */
+        const int k = 2*i;
+        if (k < len4) {
+            tmp.re = -src[ len4 + k] + src[1*len4 - 1 - k];
+            tmp.im = -src[ len3 + k] - src[1*len3 - 1 - k];
+        } else {
+            tmp.re = -src[ len4 + k] - src[5*len4 - 1 - k];
+            tmp.im =  src[-len4 + k] - src[1*len3 - 1 - k];
+        }
+        CMUL(z[s->revtab[i]].im, z[s->revtab[i]].re, tmp.re, tmp.im,
+             exp[i].re, exp[i].im);
+    }
+
+    fftp(z);
+
+    for (int i = 0; i < len8; i++) {
+        const int i0 = len8 + i, i1 = len8 - i - 1;
+        FFTComplex src1 = { z[i1].re, z[i1].im };
+        FFTComplex src0 = { z[i0].re, z[i0].im };
+
+        CMUL(dst[2*i1*stride + stride], dst[2*i0*stride], src0.re, src0.im,
+             exp[i0].im, exp[i0].re);
+        CMUL(dst[2*i0*stride + stride], dst[2*i1*stride], src1.re, src1.im,
+             exp[i1].im, exp[i1].re);
+    }
+}
+
+/* Calculates the modular multiplicative inverse, not fast, replace */
+static int mulinv(int n, int m)
+{
+    n = n % m;
+    for (int x = 1; x < m; x++)
+        if (((n * x) % m) == 1)
+            return x;
+    av_assert0(0); /* Never reached */
+}
+
+/* Guaranteed to work for any n, m where gcd(n, m) == 1 */
+static int gen_compound_mapping(AVTXContext *s, int n, int m, int inv,
+                                enum AVTXType type)
+{
+    int *in_map, *out_map;
+    const int len   = n*m;
+    const int m_inv = mulinv(m, n);
+    const int n_inv = mulinv(n, m);
+    const int mdct  = type == AV_TX_FLOAT_MDCT;
+
+    if (!(s->pfatab = av_malloc(2*len*sizeof(*s->pfatab))))
+        return AVERROR(ENOMEM);
+
+    in_map  = s->pfatab;
+    out_map = s->pfatab + n*m;
+
+    /* Ruritanian map for input, CRT map for output, can be swapped */
+    for (int j = 0; j < m; j++) {
+        for (int i = 0; i < n; i++) {
+            /* Shifted by 1 to simplify forward MDCTs */
+            in_map[j*n + i] = ((i*m + j*n) % len) << mdct;
+            out_map[(i*m*m_inv + j*n*n_inv) % len] = i*m + j;
+        }
+    }
+
+    /* Change transform direction by reversing all ACs */
+    if (inv) {
+        for (int i = 0; i < m; i++) {
+            int *in = &in_map[i*n + 1]; /* Skip the DC */
+            for (int j = 0; j < ((n - 1) >> 1); j++)
+                FFSWAP(int, in[j], in[n - j - 2]);
+        }
+    }
+
+    /* Our 15-point transform is also a compound one, so embed its input map */
+    if (n == 15) {
+        for (int k = 0; k < m; k++) {
+            int tmp[15];
+            memcpy(tmp, &in_map[k*15], 15*sizeof(*tmp));
+            for (int i = 0; i < 5; i++) {
+                for (int j = 0; j < 3; j++)
+                    in_map[k*15 + i*3 + j] = tmp[(i*3 + j*5) % 15];
+            }
+        }
+    }
+
+    return 0;
+}
+
+static int split_radix_permutation(int i, int n, int inverse)
+{
+    int m;
+    if (n <= 2)
+        return i & 1;
+    m = n >> 1;
+    if (!(i & m))
+        return split_radix_permutation(i, m, inverse)*2;
+    m >>= 1;
+    if (inverse == !(i & m))
+        return split_radix_permutation(i, m, inverse)*4 + 1;
+    else
+        return split_radix_permutation(i, m, inverse)*4 - 1;
+}
+
+static int get_ptwo_revtab(AVTXContext *s, int m, int inv)
+{
+    if (!(s->revtab = av_malloc(m*sizeof(*s->revtab))))
+        return AVERROR(ENOMEM);
+
+    /* Default */
+    for (int i = 0; i < m; i++) {
+        int k = -split_radix_permutation(i, m, inv) & (m - 1);
+        s->revtab[k] = i;
+    }
+
+    return 0;
+}
+
+static int gen_mdct_exptab(AVTXContext *s, int len4, double scale)
+{
+    const double theta = (scale < 0 ? len4 : 0) + 1.0/8.0;
+
+    if (!(s->exptab = av_malloc_array(len4, sizeof(*s->exptab))))
+        return AVERROR(ENOMEM);
+
+    scale = sqrt(fabs(scale));
+    for (int i = 0; i < len4; i++) {
+        const double alpha = M_PI_2 * (i + theta) / len4;
+        s->exptab[i].re = cos(alpha) * scale;
+        s->exptab[i].im = sin(alpha) * scale;
+    }
+
+    return 0;
+}
+
+av_cold void av_tx_uninit(AVTXContext **ctx)
+{
+    if (!ctx)
+        return;
+
+    av_free((*ctx)->pfatab);
+    av_free((*ctx)->exptab);
+    av_free((*ctx)->revtab);
+    av_free((*ctx)->tmp);
+
+    av_freep(ctx);
+}
+
+static int init_mdct_fft(AVTXContext *s, av_tx_fn *tx, enum AVTXType type,
+                         int inv, int len, const void *scale, uint64_t flags)
+{
+    int err, n = 1, m = 1, max_ptwo = 1 << (FF_ARRAY_ELEMS(fft_dispatch) + 1);
+
+    if (type == AV_TX_FLOAT_MDCT)
+        len >>= 1;
+
+#define CHECK_FACTOR(DST, FACTOR, SRC)                                         \
+    if (DST == 1 && !(SRC % FACTOR)) {                                         \
+        DST = FACTOR;                                                          \
+        SRC /= FACTOR;                                                         \
+    }
+    CHECK_FACTOR(n, 15, len)
+    CHECK_FACTOR(n,  5, len)
+    CHECK_FACTOR(n,  3, len)
+#undef CHECK_NPTWO_FACTOR
+
+    /* len must be a power of two now */
+    if (!(len & (len - 1)) && len >= 4 && len <= max_ptwo) {
+        m = len;
+        len = 1;
+    }
+
+    /* Filter out direct 3, 5 and 15 transforms, too niche */
+    if (len > 1 || m == 1) {
+        av_log(NULL, AV_LOG_ERROR, "Unsupported transform size: n = %i, "
+               "m = %i, residual = %i!\n", n, m, len);
+        return AVERROR(EINVAL);
+    } else if (n > 1 && m > 1) { /* 2D transform case */
+        if ((err = gen_compound_mapping(s, n, m, inv, type)))
+            return err;
+        if (!(s->tmp = av_malloc(n*m*sizeof(*s->tmp))))
+            return AVERROR(ENOMEM);
+        *tx = n == 3 ? compound_fft_3xM :
+              n == 5 ? compound_fft_5xM :
+                       compound_fft_15xM;
+        if (type == AV_TX_FLOAT_MDCT)
+            *tx = n == 3 ? inv ? compound_imdct_3xM  : compound_mdct_3xM :
+                  n == 5 ? inv ? compound_imdct_5xM  : compound_mdct_5xM :
+                           inv ? compound_imdct_15xM : compound_mdct_15xM;
+    } else { /* Direct transform case */
+        *tx = monolithic_fft;
+        if (type == AV_TX_FLOAT_MDCT)
+            *tx = inv ? monolithic_imdct : monolithic_mdct;
+    }
+
+    if (n != 1)
+        ff_thread_once(&tabs_53_once, ff_init_53_tabs);
+    if (m != 1) {
+        get_ptwo_revtab(s, m, inv);
+        for (int i = 4; i <= av_log2(m); i++)
+            ff_init_ff_cos_tabs(i);
+    }
+
+    if (type == AV_TX_FLOAT_MDCT)
+        if ((err = gen_mdct_exptab(s, n*m, *((float *)scale))))
+            return err;
+
+    s->n = n;
+    s->m = m;
+
+    return 0;
+}
+
+av_cold int av_tx_init(AVTXContext **ctx, av_tx_fn *tx, enum AVTXType type,
+                       int inv, int len, const void *scale, uint64_t flags)
+{
+    int err;
+    AVTXContext *s = av_mallocz(sizeof(*s));
+    if (!s)
+        return AVERROR(ENOMEM);
+
+    switch (type) {
+    case AV_TX_FLOAT_FFT:
+    case AV_TX_FLOAT_MDCT:
+        if ((err = init_mdct_fft(s, tx, type, inv, len, scale, flags)))
+            goto fail;
+        break;
+    default:
+        err = AVERROR(EINVAL);
+        goto fail;
+    }
+
+    *ctx = s;
+
+    return 0;
+
+fail:
+    av_tx_uninit(&s);
+    *tx = NULL;
+    return err;
+}