githubmirror/FFmpeg

libavutil/tx.c
803 строки30 KB
Ruiling Song
avutil/tx: should check against (*ctx)
17 май 2019, 00:25
17 май 2019, 00:2565646db
/*
 * 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 < 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].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;
}