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/******************************************************************************
*
* 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)
{
/* cos( -2Pi n/5 ), sin( -2Pi n/5 ) for n = {1, 2} */
static const lc3_intfloat_t cos1 = LC3_INTFLOAT_C( 0.3090169944, 31);
static const lc3_intfloat_t cos2 = LC3_INTFLOAT_C(-0.8090169944, 31);
static const lc3_intfloat_t sin1 = LC3_INTFLOAT_C(-0.9510565163, 31);
static const lc3_intfloat_t sin2 = LC3_INTFLOAT_C(-0.5877852523, 31);
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 + lc3_shr(
lc3_mul(s14.re, cos1) - lc3_mul(d14.im, sin1) +
lc3_mul(s23.re, cos2) - lc3_mul(d23.im, sin2), 31);
y[1].im = x[0].im + lc3_shr(
lc3_mul(s14.im, cos1) + lc3_mul(d14.re, sin1) +
lc3_mul(s23.im, cos2) + lc3_mul(d23.re, sin2), 31);
y[2].re = x[0].re + lc3_shr(
lc3_mul(s14.re, cos2) - lc3_mul(d14.im, sin2) +
lc3_mul(s23.re, cos1) + lc3_mul(d23.im, sin1), 31);
y[2].im = x[0].im + lc3_shr(
lc3_mul(s14.im, cos2) + lc3_mul(d14.re, sin2) +
lc3_mul(s23.im, cos1) - lc3_mul(d23.re, sin1), 31);
y[3].re = x[0].re + lc3_shr(
lc3_mul(s14.re, cos2) + lc3_mul(d14.im, sin2) +
lc3_mul(s23.re, cos1) - lc3_mul(d23.im, sin1), 31);
y[3].im = x[0].im + lc3_shr(
lc3_mul(s14.im, cos2) - lc3_mul(d14.re, sin2) +
lc3_mul(s23.im, cos1) + lc3_mul(d23.re, sin1), 31);
y[4].re = x[0].re + lc3_shr(
lc3_mul(s14.re, cos1) + lc3_mul(d14.im, sin1) +
lc3_mul(s23.re, cos2) + lc3_mul(d23.im, sin2), 31);
y[4].im = x[0].im + lc3_shr(
lc3_mul(s14.im, cos1) - lc3_mul(d14.re, sin1) +
lc3_mul(s23.im, cos2) - lc3_mul(d23.re, sin2), 31);
}
}
#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 + lc3_shr(
lc3_mul(x1->re, w0[j][0].re) - lc3_mul(x1->im, w0[j][0].im) +
lc3_mul(x2->re, w0[j][1].re) - lc3_mul(x2->im, w0[j][1].im), 31);
y0[j].im = x0->im + lc3_shr(
lc3_mul(x1->im, w0[j][0].re) + lc3_mul(x1->re, w0[j][0].im) +
lc3_mul(x2->im, w0[j][1].re) + lc3_mul(x2->re, w0[j][1].im), 31);
y1[j].re = x0->re + lc3_shr(
lc3_mul(x1->re, w1[j][0].re) - lc3_mul(x1->im, w1[j][0].im) +
lc3_mul(x2->re, w1[j][1].re) - lc3_mul(x2->im, w1[j][1].im), 31);
y1[j].im = x0->im + lc3_shr(
lc3_mul(x1->im, w1[j][0].re) + lc3_mul(x1->re, w1[j][0].im) +
lc3_mul(x2->im, w1[j][1].re) + lc3_mul(x2->re, w1[j][1].im), 31);
y2[j].re = x0->re + lc3_shr(
lc3_mul(x1->re, w2[j][0].re) - lc3_mul(x1->im, w2[j][0].im) +
lc3_mul(x2->re, w2[j][1].re) - lc3_mul(x2->im, w2[j][1].im), 31);
y2[j].im = x0->im + lc3_shr(
lc3_mul(x1->im, w2[j][0].re) + lc3_mul(x1->re, w2[j][0].im) +
lc3_mul(x2->im, w2[j][1].re) + lc3_mul(x2->re, w2[j][1].im), 31);
}
}
#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 + lc3_shr(
lc3_mul(x1->re, w[j].re) - lc3_mul(x1->im, w[j].im), 31);
y0[j].im = x0->im + lc3_shr(
lc3_mul(x1->im, w[j].re) + lc3_mul(x1->re, w[j].im), 31);
y1[j].re = x0->re - lc3_shr(
lc3_mul(x1->re, w[j].re) - lc3_mul(x1->im, w[j].im), 31);
y1[j].im = x0->im - lc3_shr(
lc3_mul(x1->im, w[j].re) + lc3_mul(x1->re, w[j].im), 31);
}
}
}
#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
* 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 = 40, 80, 160 n3 = 0, n2 = [3..5]
* n = 30, 60, 120, 240 n3 = 1, n2 = [1..4]
* 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 (size of the transform)
* 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 lc3_intfloat_t *x, lc3_intfloat_t *d, lc3_intfloat_t *y)
{
int ns = LC3_NS(dt, sr), nd = LC3_ND(dt, sr);
const lc3_intfloat_t *w0 = lc3_mdct_win[dt][sr], *w1 = w0 + ns;
const lc3_intfloat_t *w2 = w1, *w3 = w2 + nd;
const lc3_intfloat_t *x0 = x + ns-nd, *x1 = x0;
lc3_intfloat_t *y0 = y + ns/2, *y1 = y0;
lc3_intfloat_t *d0 = d, *d1 = d + nd;
while (x1 > x) {
*(--y0) = lc3_shr( lc3_mul(*(d0 ), *(w0++)) -
lc3_mul(*(--x1), *(--w1)), 30 );
*(y1++) = lc3_shr( lc3_mul(*(d0++) = *(x0++), *(w2++)), 30 );
*(--y0) = lc3_shr( lc3_mul(*(d0 ), *(w0++)) -
lc3_mul(*(--x1), *(--w1)), 30 );
*(y1++) = lc3_shr( lc3_mul(*(d0++) = *(x0++), *(w2++)), 30 );
}
for (x1 += ns; x0 < x1; ) {
*(--y0) = lc3_shr( lc3_mul(*(d0 ), *(w0++)) -
lc3_mul(*(--d1), *(--w1)), 30 );
*(y1++) = lc3_shr( lc3_mul(*(d0++) = *(x0++), *(w2++)) +
lc3_mul(*(d1 ) = *(--x1), *(--w3)), 30 );
*(--y0) = lc3_shr( lc3_mul(*(d0 ), *(w0++)) -
lc3_mul(*(--d1), *(--w1)), 30 );
*(y1++) = lc3_shr( lc3_mul(*(d0++) = *(x0++), *(w2++)) +
lc3_mul(*(d1 ) = *(--x1), *(--w3)), 30 );
}
}
/**
* Pre-rotate and scale MDCT of N/2 points, before 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 lc3_intfloat_t *x, struct lc3_complex *y)
{
int n4 = def->n4;
const lc3_intfloat_t *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 = lc3_shr( - lc3_mul(*(--x1), uw.re) + lc3_mul(*x0, uw.im), 31 );
u.im = lc3_shr( lc3_mul(*(x0++), uw.re) + lc3_mul(*x1, uw.im), 31 );
struct lc3_complex v, vw = *(--w1);
v.re = lc3_shr( - lc3_mul(*(--x1), vw.im) + lc3_mul(*x0, vw.re), 31 );
v.im = lc3_shr( - lc3_mul(*(x0++), vw.im) - lc3_mul(*x1, vw.re), 31 );
*(y0++) = u;
*(--y1) = v;
}
}
/**
* Post-rotate and scale FFT N/4 points, 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, lc3_intfloat_t *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;
lc3_intfloat_t *y0 = y + n4, *y1 = y0;
for ( ; y1 > y; x0++, x1--, w0++, w1--) {
lc3_intfloat_t u0, u1, v0, v1;
u0 = lc3_shr( lc3_mul(x0->im, w0->im) + lc3_mul(x0->re, w0->re), 31 );
u1 = lc3_shr( lc3_mul(x1->re, w1->im) - lc3_mul(x1->im, w1->re), 31 );
v0 = lc3_shr( lc3_mul(x0->re, w0->im) - lc3_mul(x0->im, w0->re), 31 );
v1 = lc3_shr( lc3_mul(x1->im, w1->im) + lc3_mul(x1->re, w1->re), 31 );
*(y0++) = u0; *(y0++) = u1;
*(--y1) = v0; *(--y1) = v1;
}
}
/**
* Pre-rotate and scale IMDCT 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 lc3_intfloat_t *x, struct lc3_complex *y)
{
int n4 = def->n4;
const lc3_intfloat_t *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) {
lc3_intfloat_t u0 = *(x0++), u1 = *(--x1);
lc3_intfloat_t v0 = *(x0++), v1 = *(--x1);
struct lc3_complex uw = *(w0++), vw = *(--w1);
(y0 )->re = lc3_shr( - lc3_mul(u0, uw.re) - lc3_mul(u1, uw.im), 31 );
(y0++)->im = lc3_shr( - lc3_mul(u1, uw.re) + lc3_mul(u0, uw.im), 31 );
(--y1)->re = lc3_shr( - lc3_mul(v1, vw.re) - lc3_mul(v0, vw.im), 31 );
( y1)->im = lc3_shr( - lc3_mul(v0, vw.re) + lc3_mul(v1, vw.im), 31 );
}
}
/**
* Post-rotate and scale FFT N/4 points, 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, lc3_intfloat_t *y)
{
int n4 = def->n4;
const struct lc3_complex *w0 = def->w, *w1 = w0 + n4;
const struct lc3_complex *x0 = x, *x1 = x0 + n4;
lc3_intfloat_t *y0 = y, *y1 = y0 + 2*n4;
while (x0 < x1) {
struct lc3_complex uz = *(x0++), vz = *(--x1);
struct lc3_complex uw = *(w0++), vw = *(--w1);
*(y0++) = lc3_shr( lc3_mul(uz.re, uw.im) - lc3_mul(uz.im, uw.re), 31 );
*(--y1) = lc3_shr( lc3_mul(uz.re, uw.re) + lc3_mul(uz.im, uw.im), 31 );
*(--y1) = lc3_shr( lc3_mul(vz.re, vw.im) - lc3_mul(vz.im, vw.re), 31 );
*(y0++) = lc3_shr( lc3_mul(vz.re, vw.re) + lc3_mul(vz.im, vw.im), 31 );
}
}
/**
* 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 lc3_intfloat_t *x, lc3_intfloat_t *d, lc3_intfloat_t *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 ] */
int n4 = LC3_NS(dt, sr) >> 1, nd = LC3_ND(dt, sr);
const lc3_intfloat_t *w2 = lc3_mdct_win[dt][sr], *w0 = w2 + 3*n4, *w1 = w0;
const lc3_intfloat_t *x0 = d + nd-n4, *x1 = x0;
lc3_intfloat_t *y0 = y + nd-n4, *y1 = y0, *y2 = d + nd, *y3 = d;
while (y0 > y) {
*(--y0) = *(--x0) - lc3_shr( lc3_mul(*(x ), *(w1++)), 30 );
*(y1++) = *(x1++) + lc3_shr( lc3_mul(*(x++), *(--w0)), 30 );
*(--y0) = *(--x0) - lc3_shr( lc3_mul(*(x ), *(w1++)), 30 );
*(y1++) = *(x1++) + lc3_shr( lc3_mul(*(x++), *(--w0)), 30 );
}
while (y1 < y + nd) {
*(y1++) = *(x1++) + lc3_shr( lc3_mul(*(x++), *(--w0)), 30 );
*(y1++) = *(x1++) + lc3_shr( lc3_mul(*(x++), *(--w0)), 30 );
}
while (y1 < y + 2*n4) {
*(y1++) = lc3_shr( lc3_mul(*(x ), *(--w0)), 30 );
*(--y2) = lc3_shr( lc3_mul(*(x++), *(w2++)), 30 );
*(y1++) = lc3_shr( lc3_mul(*(x ), *(--w0)), 30 );
*(--y2) = lc3_shr( lc3_mul(*(x++), *(w2++)), 30 );
}
while (y2 > y3) {
*(y3++) = lc3_shr( lc3_mul(*(x ), *(--w0)), 30 );
*(--y2) = lc3_shr( lc3_mul(*(x++), *(w2++)), 30 );
*(y3++) = lc3_shr( lc3_mul(*(x ), *(--w0)), 30 );
*(--y2) = lc3_shr( lc3_mul(*(x++), *(w2++)), 30 );
}
}
/**
* Forward MDCT transformation
*/
void lc3_mdct_forward(
enum lc3_dt dt, enum lc3_srate sr, enum lc3_srate sr_dst,
const lc3_intfloat_t *x, lc3_intfloat_t *d, lc3_intfloat_t *y)
{
const struct lc3_mdct_rot_def *rot = lc3_mdct_rot[dt][sr];
int nf = LC3_NS(dt, sr_dst);
int ns = LC3_NS(dt, sr);
struct lc3_complex buffer[ns/2];
struct lc3_complex *z = (struct lc3_complex *)y;
union { lc3_intfloat_t *s; struct lc3_complex *z; } u = { .z = buffer };
mdct_window(dt, sr, x, d, u.s);
mdct_pre_fft(rot, u.s, u.z);
u.z = fft(u.z, ns/2, u.z, z);
mdct_post_fft(rot, u.z, y);
if (ns != nf) abort(); // TODO: Rescale
}
/**
* Inverse MDCT transformation
*/
void lc3_mdct_inverse(enum lc3_dt dt, enum lc3_srate sr,
enum lc3_srate sr_src, const lc3_intfloat_t *x,
lc3_intfloat_t *d, lc3_intfloat_t *y)
{
const struct lc3_mdct_rot_def *rot = lc3_mdct_rot[dt][sr];
int nf = LC3_NS(dt, sr_src);
int ns = LC3_NS(dt, sr);
struct lc3_complex buffer[ns/2];
struct lc3_complex *z = (struct lc3_complex *)y;
union { lc3_intfloat_t *s; 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.s);
imdct_window(dt, sr, u.s, d, y);
if (ns != nf) abort(); // TODO: Rescale
}