/******************************************************************************
*
* Copyright 2022 Google LLC
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at:
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
******************************************************************************/
#include "mdct.h"
#include "tables.h"
#include "mdct_neon.h"
/* ----------------------------------------------------------------------------
* FFT processing
* -------------------------------------------------------------------------- */
/**
* FFT 5 Points
* x, y Input and output coefficients, of size 5xn
* n Number of interleaved transform to perform (n % 2 = 0)
*/
#ifndef fft_5
LC3_HOT static inline void fft_5(
const struct lc3_complex *x, struct lc3_complex *y, int n)
{
static const float cos1 = 0.3090169944; /* cos(-2Pi 1/5) */
static const float cos2 = -0.8090169944; /* cos(-2Pi 2/5) */
static const float sin1 = -0.9510565163; /* sin(-2Pi 1/5) */
static const float sin2 = -0.5877852523; /* sin(-2Pi 2/5) */
for (int i = 0; i < n; i++, x++, y+= 5) {
struct lc3_complex s14 =
{ x[1*n].re + x[4*n].re, x[1*n].im + x[4*n].im };
struct lc3_complex d14 =
{ x[1*n].re - x[4*n].re, x[1*n].im - x[4*n].im };
struct lc3_complex s23 =
{ x[2*n].re + x[3*n].re, x[2*n].im + x[3*n].im };
struct lc3_complex d23 =
{ x[2*n].re - x[3*n].re, x[2*n].im - x[3*n].im };
y[0].re = x[0].re + s14.re + s23.re;
y[0].im = x[0].im + s14.im + s23.im;
y[1].re = x[0].re + s14.re * cos1 - d14.im * sin1
+ s23.re * cos2 - d23.im * sin2;
y[1].im = x[0].im + s14.im * cos1 + d14.re * sin1
+ s23.im * cos2 + d23.re * sin2;
y[2].re = x[0].re + s14.re * cos2 - d14.im * sin2
+ s23.re * cos1 + d23.im * sin1;
y[2].im = x[0].im + s14.im * cos2 + d14.re * sin2
+ s23.im * cos1 - d23.re * sin1;
y[3].re = x[0].re + s14.re * cos2 + d14.im * sin2
+ s23.re * cos1 - d23.im * sin1;
y[3].im = x[0].im + s14.im * cos2 - d14.re * sin2
+ s23.im * cos1 + d23.re * sin1;
y[4].re = x[0].re + s14.re * cos1 + d14.im * sin1
+ s23.re * cos2 + d23.im * sin2;
y[4].im = x[0].im + s14.im * cos1 - d14.re * sin1
+ s23.im * cos2 - d23.re * sin2;
}
}
#endif /* fft_5 */
/**
* FFT Butterfly 3 Points
* x, y Input and output coefficients
* twiddles Twiddles factors, determine size of transform
* n Number of interleaved transforms
*/
#ifndef fft_bf3
LC3_HOT static inline void fft_bf3(
const struct lc3_fft_bf3_twiddles *twiddles,
const struct lc3_complex *x, struct lc3_complex *y, int n)
{
int n3 = twiddles->n3;
const struct lc3_complex (*w0)[2] = twiddles->t;
const struct lc3_complex (*w1)[2] = w0 + n3, (*w2)[2] = w1 + n3;
const struct lc3_complex *x0 = x, *x1 = x0 + n*n3, *x2 = x1 + n*n3;
struct lc3_complex *y0 = y, *y1 = y0 + n3, *y2 = y1 + n3;
for (int i = 0; i < n; i++, y0 += 3*n3, y1 += 3*n3, y2 += 3*n3)
for (int j = 0; j < n3; j++, x0++, x1++, x2++) {
y0[j].re = x0->re + x1->re * w0[j][0].re - x1->im * w0[j][0].im
+ x2->re * w0[j][1].re - x2->im * w0[j][1].im;
y0[j].im = x0->im + x1->im * w0[j][0].re + x1->re * w0[j][0].im
+ x2->im * w0[j][1].re + x2->re * w0[j][1].im;
y1[j].re = x0->re + x1->re * w1[j][0].re - x1->im * w1[j][0].im
+ x2->re * w1[j][1].re - x2->im * w1[j][1].im;
y1[j].im = x0->im + x1->im * w1[j][0].re + x1->re * w1[j][0].im
+ x2->im * w1[j][1].re + x2->re * w1[j][1].im;
y2[j].re = x0->re + x1->re * w2[j][0].re - x1->im * w2[j][0].im
+ x2->re * w2[j][1].re - x2->im * w2[j][1].im;
y2[j].im = x0->im + x1->im * w2[j][0].re + x1->re * w2[j][0].im
+ x2->im * w2[j][1].re + x2->re * w2[j][1].im;
}
}
#endif /* fft_bf3 */
/**
* FFT Butterfly 2 Points
* twiddles Twiddles factors, determine size of transform
* x, y Input and output coefficients
* n Number of interleaved transforms
*/
#ifndef fft_bf2
LC3_HOT static inline void fft_bf2(
const struct lc3_fft_bf2_twiddles *twiddles,
const struct lc3_complex *x, struct lc3_complex *y, int n)
{
int n2 = twiddles->n2;
const struct lc3_complex *w = twiddles->t;
const struct lc3_complex *x0 = x, *x1 = x0 + n*n2;
struct lc3_complex *y0 = y, *y1 = y0 + n2;
for (int i = 0; i < n; i++, y0 += 2*n2, y1 += 2*n2) {
for (int j = 0; j < n2; j++, x0++, x1++) {
y0[j].re = x0->re + x1->re * w[j].re - x1->im * w[j].im;
y0[j].im = x0->im + x1->im * w[j].re + x1->re * w[j].im;
y1[j].re = x0->re - x1->re * w[j].re + x1->im * w[j].im;
y1[j].im = x0->im - x1->im * w[j].re - x1->re * w[j].im;
}
}
}
#endif /* fft_bf2 */
/**
* Perform FFT
* x, y0, y1 Input, and 2 scratch buffers of size `n`
* n Number of points 30, 40, 60, 80, 90, 120, 160, 180, 240, 480
* return The buffer `y0` or `y1` that hold the result
*
* Input `x` can be the same as the `y0` second scratch buffer
*/
static struct lc3_complex *fft(const struct lc3_complex *x, int n,
struct lc3_complex *y0, struct lc3_complex *y1)
{
struct lc3_complex *y[2] = { y1, y0 };
int i2, i3, is = 0;
/* The number of points `n` can be decomposed as :
*
* n = 5^1 * 3^n3 * 2^n2
*
* for n = 10, 20, 40, 80, 160 n3 = 0, n2 = [1..5]
* n = 30, 60, 120, 240, 480 n3 = 1, n2 = [1..5]
* n = 90, 180 n3 = 2, n2 = [1..2]
*
* Note that the expression `n & (n-1) == 0` is equivalent
* to the check that `n` is a power of 2. */
fft_5(x, y[is], n /= 5);
for (i3 = 0; n & (n-1); i3++, is ^= 1)
fft_bf3(lc3_fft_twiddles_bf3[i3], y[is], y[is ^ 1], n /= 3);
for (i2 = 0; n > 1; i2++, is ^= 1)
fft_bf2(lc3_fft_twiddles_bf2[i2][i3], y[is], y[is ^ 1], n >>= 1);
return y[is];
}
/* ----------------------------------------------------------------------------
* MDCT processing
* -------------------------------------------------------------------------- */
/**
* Windowing of samples before MDCT
* dt, sr Duration and samplerate
* x, y Input current and delayed samples
* y, d Output windowed samples, and delayed ones
*/
LC3_HOT static void mdct_window(
enum lc3_dt dt, enum lc3_srate sr,
const float *x, float *d, float *y)
{
const float *win = lc3_mdct_win[dt][sr];
int ns = lc3_ns(dt, sr), nd = lc3_nd(dt, sr);
const float *w0 = win, *w1 = w0 + ns;
const float *w2 = w1, *w3 = w2 + nd;
const float *x0 = x + ns-nd, *x1 = x0;
float *y0 = y + ns/2, *y1 = y0;
float *d0 = d, *d1 = d + nd;
while (x1 > x) {
*(--y0) = *d0 * *(w0++) - *(--x1) * *(--w1);
*(y1++) = (*(d0++) = *(x0++)) * *(w2++);
*(--y0) = *d0 * *(w0++) - *(--x1) * *(--w1);
*(y1++) = (*(d0++) = *(x0++)) * *(w2++);
}
for (x1 += ns; x0 < x1; ) {
*(--y0) = *d0 * *(w0++) - *(--d1) * *(--w1);
*(y1++) = (*(d0++) = *(x0++)) * *(w2++) + (*d1 = *(--x1)) * *(--w3);
*(--y0) = *d0 * *(w0++) - *(--d1) * *(--w1);
*(y1++) = (*(d0++) = *(x0++)) * *(w2++) + (*d1 = *(--x1)) * *(--w3);
}
}
/**
* Pre-rotate MDCT coefficients of N/2 points, before FFT N/4 points FFT
* def Size and twiddles factors
* x, y Input and output coefficients
*
* `x` and y` can be the same buffer
*/
LC3_HOT static void mdct_pre_fft(const struct lc3_mdct_rot_def *def,
const float *x, struct lc3_complex *y)
{
int n4 = def->n4;
const float *x0 = x, *x1 = x0 + 2*n4;
const struct lc3_complex *w0 = def->w, *w1 = w0 + n4;
struct lc3_complex *y0 = y, *y1 = y0 + n4;
while (x0 < x1) {
struct lc3_complex u, uw = *(w0++);
u.re = - *(--x1) * uw.re + *x0 * uw.im;
u.im = *(x0++) * uw.re + *x1 * uw.im;
struct lc3_complex v, vw = *(--w1);
v.re = - *(--x1) * vw.im + *x0 * vw.re;
v.im = - *(x0++) * vw.im - *x1 * vw.re;
*(y0++) = u;
*(--y1) = v;
}
}
/**
* Post-rotate FFT N/4 points coefficients, resulting MDCT N points
* def Size and twiddles factors
* x, y Input and output coefficients
*
* `x` and y` can be the same buffer
*/
LC3_HOT static void mdct_post_fft(const struct lc3_mdct_rot_def *def,
const struct lc3_complex *x, float *y)
{
int n4 = def->n4, n8 = n4 >> 1;
const struct lc3_complex *w0 = def->w + n8, *w1 = w0 - 1;
const struct lc3_complex *x0 = x + n8, *x1 = x0 - 1;
float *y0 = y + n4, *y1 = y0;
for ( ; y1 > y; x0++, x1--, w0++, w1--) {
float u0 = x0->im * w0->im + x0->re * w0->re;
float u1 = x1->re * w1->im - x1->im * w1->re;
float v0 = x0->re * w0->im - x0->im * w0->re;
float v1 = x1->im * w1->im + x1->re * w1->re;
*(y0++) = u0; *(y0++) = u1;
*(--y1) = v0; *(--y1) = v1;
}
}
/**
* Pre-rotate IMDCT coefficients of N points, before FFT N/4 points FFT
* def Size and twiddles factors
* x, y Input and output coefficients
*
* `x` and `y` can be the same buffer
* The real and imaginary parts of `y` are swapped,
* to operate on FFT instead of IFFT
*/
LC3_HOT static void imdct_pre_fft(const struct lc3_mdct_rot_def *def,
const float *x, struct lc3_complex *y)
{
int n4 = def->n4;
const float *x0 = x, *x1 = x0 + 2*n4;
const struct lc3_complex *w0 = def->w, *w1 = w0 + n4;
struct lc3_complex *y0 = y, *y1 = y0 + n4;
while (x0 < x1) {
float u0 = *(x0++), u1 = *(--x1);
float v0 = *(x0++), v1 = *(--x1);
struct lc3_complex uw = *(w0++), vw = *(--w1);
(y0 )->re = - u0 * uw.re - u1 * uw.im;
(y0++)->im = - u1 * uw.re + u0 * uw.im;
(--y1)->re = - v1 * vw.re - v0 * vw.im;
( y1)->im = - v0 * vw.re + v1 * vw.im;
}
}
/**
* Post-rotate FFT N/4 points coefficients, resulting IMDCT N points
* def Size and twiddles factors
* x, y Input and output coefficients
*
* `x` and y` can be the same buffer
* The real and imaginary parts of `x` are swapped,
* to operate on FFT instead of IFFT
*/
LC3_HOT static void imdct_post_fft(const struct lc3_mdct_rot_def *def,
const struct lc3_complex *x, float *y)
{
int n4 = def->n4;
const struct lc3_complex *w0 = def->w, *w1 = w0 + n4;
const struct lc3_complex *x0 = x, *x1 = x0 + n4;
float *y0 = y, *y1 = y0 + 2*n4;
while (x0 < x1) {
struct lc3_complex uz = *(x0++), vz = *(--x1);
struct lc3_complex uw = *(w0++), vw = *(--w1);
*(y0++) = uz.re * uw.im - uz.im * uw.re;
*(--y1) = uz.re * uw.re + uz.im * uw.im;
*(--y1) = vz.re * vw.im - vz.im * vw.re;
*(y0++) = vz.re * vw.re + vz.im * vw.im;
}
}
/**
* Apply windowing of samples
* dt, sr Duration and samplerate
* x, d Middle half of IMDCT coefficients and delayed samples
* y, d Output samples and delayed ones
*/
LC3_HOT static void imdct_window(
enum lc3_dt dt, enum lc3_srate sr,
const float *x, float *d, float *y)
{
/* The full MDCT coefficients is given by symmetry :
* T[ 0 .. n/4-1] = -half[n/4-1 .. 0 ]
* T[ n/4 .. n/2-1] = half[0 .. n/4-1]
* T[ n/2 .. 3n/4-1] = half[n/4 .. n/2-1]
* T[3n/4 .. n-1] = half[n/2-1 .. n/4 ] */
const float *win = lc3_mdct_win[dt][sr];
int n4 = lc3_ns(dt, sr) >> 1, nd = lc3_nd(dt, sr);
const float *w2 = win, *w0 = w2 + 3*n4, *w1 = w0;
const float *x0 = d + nd-n4, *x1 = x0;
float *y0 = y + nd-n4, *y1 = y0, *y2 = d + nd, *y3 = d;
while (y0 > y) {
*(--y0) = *(--x0) - *(x ) * *(w1++);
*(y1++) = *(x1++) + *(x++) * *(--w0);
*(--y0) = *(--x0) - *(x ) * *(w1++);
*(y1++) = *(x1++) + *(x++) * *(--w0);
}
while (y1 < y + nd) {
*(y1++) = *(x1++) + *(x++) * *(--w0);
*(y1++) = *(x1++) + *(x++) * *(--w0);
}
while (y1 < y + 2*n4) {
*(y1++) = *(x ) * *(--w0);
*(--y2) = *(x++) * *(w2++);
*(y1++) = *(x ) * *(--w0);
*(--y2) = *(x++) * *(w2++);
}
while (y2 > y3) {
*(y3++) = *(x ) * *(--w0);
*(--y2) = *(x++) * *(w2++);
*(y3++) = *(x ) * *(--w0);
*(--y2) = *(x++) * *(w2++);
}
}
/**
* Rescale samples
* x, n Input and count of samples, scaled as output
* scale Scale factor
*/
LC3_HOT static void rescale(float *x, int n, float f)
{
for (int i = 0; i < (n >> 2); i++) {
*(x++) *= f; *(x++) *= f;
*(x++) *= f; *(x++) *= f;
}
}
/**
* Forward MDCT transformation
*/
void lc3_mdct_forward(
enum lc3_dt dt, enum lc3_srate sr, enum lc3_srate sr_dst,
const float *x, float *d, float *y)
{
const struct lc3_mdct_rot_def *rot = lc3_mdct_rot[dt][sr];
int ns_dst = lc3_ns(dt, sr_dst);
int ns = lc3_ns(dt, sr);
struct lc3_complex buffer[LC3_MAX_NS / 2];
struct lc3_complex *z = (struct lc3_complex *)y;
union { float *f; struct lc3_complex *z; } u = { .z = buffer };
mdct_window(dt, sr, x, d, u.f);
mdct_pre_fft(rot, u.f, u.z);
u.z = fft(u.z, ns/2, u.z, z);
mdct_post_fft(rot, u.z, y);
if (ns != ns_dst)
rescale(y, ns_dst, sqrtf((float)ns_dst / ns));
}
/**
* Inverse MDCT transformation
*/
void lc3_mdct_inverse(
enum lc3_dt dt, enum lc3_srate sr, enum lc3_srate sr_src,
const float *x, float *d, float *y)
{
const struct lc3_mdct_rot_def *rot = lc3_mdct_rot[dt][sr];
int ns_src = lc3_ns(dt, sr_src);
int ns = lc3_ns(dt, sr);
struct lc3_complex buffer[LC3_MAX_NS / 2];
struct lc3_complex *z = (struct lc3_complex *)y;
union { float *f; struct lc3_complex *z; } u = { .z = buffer };
imdct_pre_fft(rot, x, z);
z = fft(z, ns/2, z, u.z);
imdct_post_fft(rot, z, u.f);
if (ns != ns_src)
rescale(u.f, ns, sqrtf((float)ns / ns_src));
imdct_window(dt, sr, u.f, d, y);
}