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aomedia / aom / 6bdc40f158f01a53e4 / . / av1 / common / pvq.c
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/*
* Copyright (c) 2001-2016, Alliance for Open Media. All rights reserved
*
* This source code is subject to the terms of the BSD 2 Clause License and
* the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
* was not distributed with this source code in the LICENSE file, you can
* obtain it at www.aomedia.org/license/software. If the Alliance for Open
* Media Patent License 1.0 was not distributed with this source code in the
* PATENTS file, you can obtain it at www.aomedia.org/license/patent.
*/
/* clang-format off */
#ifdef HAVE_CONFIG_H
# include "config.h"
#endif
#include "odintrin.h"
#include "partition.h"
#include "pvq.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Imported from encode.c in daala */
/* These are the PVQ equivalent of quantization matrices, except that
the values are per-band. */
#define OD_MASKING_DISABLED 0
#define OD_MASKING_ENABLED 1
const unsigned char OD_LUMA_QM_Q4[2][OD_QM_SIZE] = {
/* Flat quantization for PSNR. The DC component isn't 16 because the DC
magnitude compensation is done here for inter (Haar DC doesn't need it).
Masking disabled: */
{
16, 16,
16, 16, 16, 16,
16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16
},
/* The non-flat AC coefficients compensate for the non-linear scaling caused
by activity masking. The values are currently hand-tuned so that the rate
of each band remains roughly constant when enabling activity masking
on intra.
Masking enabled: */
{
16, 16,
16, 18, 28, 32,
16, 14, 20, 20, 28, 32,
16, 11, 14, 14, 17, 17, 22, 28
}
};
const unsigned char OD_CHROMA_QM_Q4[2][OD_QM_SIZE] = {
/* Chroma quantization is different because of the reduced lapping.
FIXME: Use the same matrix as luma for 4:4:4.
Masking disabled: */
{
16, 16,
16, 16, 16, 16,
16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16
},
/* The AC part is flat for chroma because it has no activity masking.
Masking enabled: */
{
16, 16,
16, 16, 16, 16,
16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16
}
};
/* No interpolation, always use od_flat_qm_q4, but use a different scale for
each plane.
FIXME: Add interpolation and properly tune chroma. */
const od_qm_entry OD_DEFAULT_QMS[2][2][OD_NPLANES_MAX] = {
/* Masking disabled */
{ { { 4, 256, OD_LUMA_QM_Q4[OD_MASKING_DISABLED] },
{ 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_DISABLED] },
{ 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_DISABLED] } },
{ { 0, 0, NULL},
{ 0, 0, NULL},
{ 0, 0, NULL} } },
/* Masking enabled */
{ { { 4, 256, OD_LUMA_QM_Q4[OD_MASKING_ENABLED] },
{ 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_ENABLED] },
{ 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_ENABLED] } },
{ { 0, 0, NULL},
{ 0, 0, NULL},
{ 0, 0, NULL} } }
};
/* Constants for the beta parameter, which controls how activity masking is
used.
beta = 1 / (1 - alpha), so when beta is 1, alpha is 0 and activity
masking is disabled. When beta is 1.5, activity masking is used. Note that
activity masking is neither used for 4x4 blocks nor for chroma. */
#define OD_BETA(b) OD_QCONST32(b, OD_BETA_SHIFT)
static const od_val16 OD_PVQ_BETA4_LUMA[1] = {OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA8_LUMA[4] = {OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA16_LUMA[7] = {OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA32_LUMA[10] = {OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA4_LUMA_MASKING[1] = {OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA8_LUMA_MASKING[4] = {OD_BETA(1.5),
OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5)};
static const od_val16 OD_PVQ_BETA16_LUMA_MASKING[7] = {OD_BETA(1.5),
OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5),
OD_BETA(1.5)};
static const od_val16 OD_PVQ_BETA32_LUMA_MASKING[10] = {OD_BETA(1.5),
OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5),
OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5)};
static const od_val16 OD_PVQ_BETA4_CHROMA[1] = {OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA8_CHROMA[4] = {OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA16_CHROMA[7] = {OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.)};
static const od_val16 OD_PVQ_BETA32_CHROMA[10] = {OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.),
OD_BETA(1.), OD_BETA(1.)};
const od_val16 *const OD_PVQ_BETA[2][OD_NPLANES_MAX][OD_TXSIZES + 1] = {
{{OD_PVQ_BETA4_LUMA, OD_PVQ_BETA8_LUMA,
OD_PVQ_BETA16_LUMA, OD_PVQ_BETA32_LUMA},
{OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA,
OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA},
{OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA,
OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA}},
{{OD_PVQ_BETA4_LUMA_MASKING, OD_PVQ_BETA8_LUMA_MASKING,
OD_PVQ_BETA16_LUMA_MASKING, OD_PVQ_BETA32_LUMA_MASKING},
{OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA,
OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA},
{OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA,
OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA}}
};
void od_interp_qm(unsigned char *out, int q, const od_qm_entry *entry1,
const od_qm_entry *entry2) {
int i;
if (entry2 == NULL || entry2->qm_q4 == NULL
|| q < entry1->interp_q << OD_COEFF_SHIFT) {
/* Use entry1. */
for (i = 0; i < OD_QM_SIZE; i++) {
out[i] = OD_MINI(255, entry1->qm_q4[i]*entry1->scale_q8 >> 8);
}
}
else if (entry1 == NULL || entry1->qm_q4 == NULL
|| q > entry2->interp_q << OD_COEFF_SHIFT) {
/* Use entry2. */
for (i = 0; i < OD_QM_SIZE; i++) {
out[i] = OD_MINI(255, entry2->qm_q4[i]*entry2->scale_q8 >> 8);
}
}
else {
/* Interpolate between entry1 and entry2. The interpolation is linear
in terms of log(q) vs log(m*scale). Considering that we're ultimately
multiplying the result it makes sense, but we haven't tried other
interpolation methods. */
double x;
const unsigned char *m1;
const unsigned char *m2;
int q1;
int q2;
m1 = entry1->qm_q4;
m2 = entry2->qm_q4;
q1 = entry1->interp_q << OD_COEFF_SHIFT;
q2 = entry2->interp_q << OD_COEFF_SHIFT;
x = (log(q)-log(q1))/(log(q2)-log(q1));
for (i = 0; i < OD_QM_SIZE; i++) {
out[i] = OD_MINI(255, (int)floor(.5 + (1./256)*exp(
x*log(m2[i]*entry2->scale_q8) + (1 - x)*log(m1[i]*entry1->scale_q8))));
}
}
}
void od_adapt_pvq_ctx_reset(od_pvq_adapt_ctx *state, int is_keyframe) {
od_pvq_codeword_ctx *ctx;
int i;
int pli;
int bs;
ctx = &state->pvq_codeword_ctx;
OD_CDFS_INIT_DYNAMIC(state->pvq_param_model[0].cdf);
OD_CDFS_INIT_DYNAMIC(state->pvq_param_model[1].cdf);
OD_CDFS_INIT_DYNAMIC(state->pvq_param_model[2].cdf);
for (i = 0; i < 2*OD_TXSIZES; i++) {
ctx->pvq_adapt[4*i + OD_ADAPT_K_Q8] = 384;
ctx->pvq_adapt[4*i + OD_ADAPT_SUM_EX_Q8] = 256;
ctx->pvq_adapt[4*i + OD_ADAPT_COUNT_Q8] = 104;
ctx->pvq_adapt[4*i + OD_ADAPT_COUNT_EX_Q8] = 128;
}
OD_CDFS_INIT_DYNAMIC(ctx->pvq_k1_cdf);
for (pli = 0; pli < OD_NPLANES_MAX; pli++) {
for (bs = 0; bs < OD_TXSIZES; bs++)
for (i = 0; i < PVQ_MAX_PARTITIONS; i++) {
state->pvq_exg[pli][bs][i] = 2 << 16;
}
}
for (i = 0; i < OD_TXSIZES*PVQ_MAX_PARTITIONS; i++) {
state->pvq_ext[i] = is_keyframe ? 24576 : 2 << 16;
}
OD_CDFS_INIT_DYNAMIC(state->pvq_gaintheta_cdf);
OD_CDFS_INIT_Q15(state->pvq_skip_dir_cdf);
OD_CDFS_INIT_DYNAMIC(ctx->pvq_split_cdf);
}
/* QMs are arranged from smallest to largest blocksizes, first for
blocks with decimation=0, followed by blocks with decimation=1.*/
int od_qm_offset(int bs, int xydec)
{
return xydec*OD_QM_STRIDE + OD_QM_OFFSET(bs);
}
#if defined(OD_FLOAT_PVQ)
#define OD_DEFAULT_MAG 1.0
#else
#define OD_DEFAULT_MAG OD_QM_SCALE
#endif
/* Initialize the quantization matrix. */
// Note: When hybrid transform and corresponding scan order is used by PVQ,
// we don't need seperate qm and qm_inv for each transform type,
// because AOM does not do magnitude compensation (i.e. simplay x16 for all coeffs).
void od_init_qm(int16_t *x, int16_t *x_inv, const int *qm) {
int i;
int j;
int16_t y[OD_TXSIZE_MAX*OD_TXSIZE_MAX];
int16_t y_inv[OD_TXSIZE_MAX*OD_TXSIZE_MAX];
int16_t *x1;
int16_t *x1_inv;
int off;
int bs;
int xydec;
for (bs = 0; bs < OD_TXSIZES; bs++) {
for (xydec = 0; xydec < 2; xydec++) {
off = od_qm_offset(bs, xydec);
x1 = x + off;
x1_inv = x_inv + off;
for (i = 0; i < 4 << bs; i++) {
for (j = 0; j < 4 << bs; j++) {
/*This will ultimately be clamped to fit in 16 bits.*/
od_val32 mag;
int16_t ytmp;
mag = OD_DEFAULT_MAG;
if (i != 0 || j != 0) {
#if defined(OD_FLOAT_PVQ)
mag /= 0.0625*qm[(i << 1 >> bs)*8 + (j << 1 >> bs)];
#else
int qmv;
qmv = qm[(i << 1 >> bs)*8 + (j << 1 >> bs)];
mag *= 16;
mag = (mag + (qmv >> 1))/qmv;
#endif
OD_ASSERT(mag > 0.0);
}
/*Convert to fit in 16 bits.*/
#if defined(OD_FLOAT_PVQ)
y[i*(4 << bs) + j] = (int16_t)OD_MINI(OD_QM_SCALE_MAX,
(int32_t)floor(.5 + mag*OD_QM_SCALE));
y_inv[i*(4 << bs) + j] = (int16_t)floor(.5
+ OD_QM_SCALE*OD_QM_INV_SCALE/(double)y[i*(4 << bs) + j]);
#else
y[i*(4 << bs) + j] = (int16_t)OD_MINI(OD_QM_SCALE_MAX, mag);
ytmp = y[i*(4 << bs) + j];
y_inv[i*(4 << bs) + j] = (int16_t)((OD_QM_SCALE*OD_QM_INV_SCALE
+ (ytmp >> 1))/ytmp);
#endif
}
}
od_raster_to_coding_order_16(x1, 4 << bs, y, 4 << bs);
od_raster_to_coding_order_16(x1_inv, 4 << bs, y_inv, 4 << bs);
}
}
}
/* Maps each possible size (n) in the split k-tokenizer to a different value.
Possible values of n are:
2, 3, 4, 7, 8, 14, 15, 16, 31, 32, 63, 64, 127, 128
Since we don't care about the order (even in the bit-stream) the simplest
ordering (implemented here) is:
14, 2, 3, 4, 7, 8, 15, 16, 31, 32, 63, 64, 127, 128 */
int od_pvq_size_ctx(int n) {
int logn;
int odd;
logn = OD_ILOG(n - 1);
odd = n & 1;
return 2*logn - 1 - odd - 7*(n == 14);
}
/* Maps a length n to a context for the (k=1, n<=16) coder, with a special
case when n is the original length (orig_length=1) of the vector (i.e. we
haven't split it yet). For orig_length=0, we use the same mapping as
od_pvq_size_ctx() up to n=16. When orig_length=1, we map lengths
7, 8, 14, 15 to contexts 8 to 11. */
int od_pvq_k1_ctx(int n, int orig_length) {
if (orig_length) return 8 + 2*(n > 8) + (n & 1);
else return od_pvq_size_ctx(n);
}
/* Indexing for the packed quantization matrices. */
int od_qm_get_index(int bs, int band) {
/* The -band/3 term is due to the fact that we force corresponding horizontal
and vertical bands to have the same quantization. */
OD_ASSERT(bs >= 0 && bs < OD_TXSIZES);
return bs*(bs + 1) + band - band/3;
}
#if !defined(OD_FLOAT_PVQ)
/*See celt/mathops.c in Opus and tools/cos_search.c.*/
static int16_t od_pvq_cos_pi_2(int16_t x)
{
int16_t x2;
x2 = OD_MULT16_16_Q15(x, x);
return OD_MINI(32767, (1073758164 - x*x + x2*(-7654 + OD_MULT16_16_Q16(x2,
16573 + OD_MULT16_16_Q16(-2529, x2)))) >> 15);
}
#endif
/*Approximates cos(x) for -pi < x < pi.
Input is in OD_THETA_SCALE.*/
od_val16 od_pvq_cos(od_val32 x) {
#if defined(OD_FLOAT_PVQ)
return cos(x);
#else
/*Wrap x around by masking, since cos is periodic.*/
x = x & 0x0001ffff;
if (x > (1 << 16)) {
x = (1 << 17) - x;
}
if (x & 0x00007fff) {
if (x < (1 << 15)) {
return od_pvq_cos_pi_2((int16_t)x);
}
else {
return -od_pvq_cos_pi_2((int16_t)(65536 - x));
}
}
else {
if (x & 0x0000ffff) {
return 0;
}
else if (x & 0x0001ffff) {
return -32767;
}
else {
return 32767;
}
}
#endif
}
/*Approximates sin(x) for 0 <= x < pi.
Input is in OD_THETA_SCALE.*/
od_val16 od_pvq_sin(od_val32 x) {
#if defined(OD_FLOAT_PVQ)
return sin(x);
#else
return od_pvq_cos(32768 - x);
#endif
}
#if !defined(OD_FLOAT_PVQ)
/* Computes an upper-bound on the number of bits required to store the L2 norm
of a vector (excluding sign). */
int od_vector_log_mag(const od_coeff *x, int n) {
int i;
int32_t sum;
sum = 0;
for (i = 0; i < n; i++) {
int16_t tmp;
tmp = x[i] >> 8;
sum += tmp*(int32_t)tmp;
}
/* We add one full bit (instead of rounding OD_ILOG() up) for safety because
the >> 8 above causes the sum to be slightly underestimated. */
return 8 + 1 + OD_ILOG(n + sum)/2;
}
#endif
/** Computes Householder reflection that aligns the reference r to the
* dimension in r with the greatest absolute value. The reflection
* vector is returned in r.
*
* @param [in,out] r reference vector to be reflected, reflection
* also returned in r
* @param [in] n number of dimensions in r
* @param [in] gr gain of reference vector
* @param [out] sign sign of reflection
* @return dimension number to which reflection aligns
**/
int od_compute_householder(od_val16 *r, int n, od_val32 gr, int *sign,
int shift) {
int m;
int i;
int s;
od_val16 maxr;
OD_UNUSED(shift);
/* Pick component with largest magnitude. Not strictly
* necessary, but it helps numerical stability */
m = 0;
maxr = 0;
for (i = 0; i < n; i++) {
if (OD_ABS(r[i]) > maxr) {
maxr = OD_ABS(r[i]);
m = i;
}
}
s = r[m] > 0 ? 1 : -1;
/* This turns r into a Householder reflection vector that would reflect
* the original r[] to e_m */
r[m] += OD_SHR_ROUND(gr*s, shift);
*sign = s;
return m;
}
#if !defined(OD_FLOAT_PVQ)
#define OD_RCP_INSHIFT 15
#define OD_RCP_OUTSHIFT 14
static od_val16 od_rcp(od_val16 x)
{
int i;
od_val16 n;
od_val16 r;
i = OD_ILOG(x) - 1;
/*n is Q15 with range [0,1).*/
n = OD_VSHR_ROUND(x, i - OD_RCP_INSHIFT) - (1 << OD_RCP_INSHIFT);
/*Start with a linear approximation:
r = 1.8823529411764706-0.9411764705882353*n.
The coefficients and the result are Q14 in the range [15420,30840].*/
r = 30840 + OD_MULT16_16_Q15(-15420, n);
/*Perform two Newton iterations:
r -= r*((r*n)-1.Q15)
= r*((r*n)+(r-1.Q15)).*/
r = r - OD_MULT16_16_Q15(r, (OD_MULT16_16_Q15(r, n) + r - 32768));
/*We subtract an extra 1 in the second iteration to avoid overflow; it also
neatly compensates for truncation error in the rest of the process.*/
r = r - (1 + OD_MULT16_16_Q15(r, OD_MULT16_16_Q15(r, n) + r - 32768));
/*r is now the Q15 solution to 2/(n+1), with a maximum relative error
of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a peak absolute
error of 1.24665/32768.*/
return OD_VSHR_ROUND(r, i - OD_RCP_OUTSHIFT);
}
#endif
/** Applies Householder reflection from compute_householder(). The
* reflection is its own inverse.
*
* @param [out] out reflected vector
* @param [in] x vector to be reflected
* @param [in] r reflection
* @param [in] n number of dimensions in x,r
*/
void od_apply_householder(od_val16 *out, const od_val16 *x, const od_val16 *r,
int n) {
int i;
od_val32 proj;
od_val16 proj_1;
od_val32 l2r;
#if !defined(OD_FLOAT_PVQ)
od_val16 proj_norm;
od_val16 l2r_norm;
od_val16 rcp;
int proj_shift;
int l2r_shift;
int outshift;
#endif
/*FIXME: Can we get l2r and/or l2r_shift from an earlier computation?*/
l2r = 0;
for (i = 0; i < n; i++) {
l2r += OD_MULT16_16(r[i], r[i]);
}
/* Apply Householder reflection */
proj = 0;
for (i = 0; i < n; i++) {
proj += OD_MULT16_16(r[i], x[i]);
}
#if defined(OD_FLOAT_PVQ)
proj_1 = proj*2./(1e-100 + l2r);
for (i = 0; i < n; i++) {
out[i] = x[i] - r[i]*proj_1;
}
#else
/*l2r_norm is [0.5, 1.0[ in Q15.*/
l2r_shift = (OD_ILOG(l2r) - 1) - 14;
l2r_norm = OD_VSHR_ROUND(l2r, l2r_shift);
rcp = od_rcp(l2r_norm);
proj_shift = (OD_ILOG(abs(proj)) - 1) - 14;
/*proj_norm is [0.5, 1.0[ in Q15.*/
proj_norm = OD_VSHR_ROUND(proj, proj_shift);
proj_1 = OD_MULT16_16_Q15(proj_norm, rcp);
/*The proj*2. in the float code becomes -1 in the final outshift.
The sign of l2r_shift is positive since we're taking the reciprocal of
l2r_norm and this is a right shift.*/
outshift = OD_MINI(30, OD_RCP_OUTSHIFT - proj_shift - 1 + l2r_shift);
if (outshift >= 0) {
for (i = 0; i < n; i++) {
int32_t tmp;
tmp = OD_MULT16_16(r[i], proj_1);
tmp = OD_SHR_ROUND(tmp, outshift);
out[i] = x[i] - tmp;
}
}
else {
/*FIXME: Can we make this case impossible?
Right now, if r[] is all zeros except for 1, 2, or 3 ones, and
if x[] is all zeros except for large values at the same position as the
ones in r[], then we can end up with a shift of -1.*/
for (i = 0; i < n; i++) {
int32_t tmp;
tmp = OD_MULT16_16(r[i], proj_1);
tmp = OD_SHL(tmp, -outshift);
out[i] = x[i] - tmp;
}
}
#endif
}
#if !defined(OD_FLOAT_PVQ)
static od_val16 od_beta_rcp(od_val16 beta){
if (beta == OD_BETA(1.))
return OD_BETA(1.);
else if (beta == OD_BETA(1.5))
return OD_BETA(1./1.5);
else {
od_val16 rcp_beta;
/*Shift by 1 less, transposing beta to range [.5, .75] and thus < 32768.*/
rcp_beta = od_rcp(beta << (OD_RCP_INSHIFT - 1 - OD_BETA_SHIFT));
return OD_SHR_ROUND(rcp_beta, OD_RCP_OUTSHIFT + 1 - OD_BETA_SHIFT);
}
}
#define OD_EXP2_INSHIFT 15
#define OD_EXP2_FRACSHIFT 15
#define OD_EXP2_OUTSHIFT 15
static const int32_t OD_EXP2_C[5] = {32768, 22709, 7913, 1704, 443};
/*Output is [1.0, 2.0) in Q(OD_EXP2_FRACSHIFT).
It does not include the integer offset, which is added in od_exp2 after the
final shift).*/
static int32_t od_exp2_frac(int32_t x)
{
return OD_MULT16_16_Q15(x, (OD_EXP2_C[1] + OD_MULT16_16_Q15(x,
(OD_EXP2_C[2] + OD_MULT16_16_Q15(x, (OD_EXP2_C[3]
+ OD_MULT16_16_Q15(x, OD_EXP2_C[4])))))));
}
/** Base-2 exponential approximation (2^x) with Q15 input and output.*/
static int32_t od_exp2(int32_t x)
{
int integer;
int32_t frac;
integer = x >> OD_EXP2_INSHIFT;
if (integer > 14)
return 0x7f000000;
else if (integer < -15)
return 0;
frac = od_exp2_frac(x - OD_SHL(integer, OD_EXP2_INSHIFT));
return OD_VSHR_ROUND(OD_EXP2_C[0] + frac, -integer) + 1;
}
#define OD_LOG2_INSHIFT 15
#define OD_LOG2_OUTSHIFT 15
#define OD_LOG2_INSCALE_1 (1./(1 << OD_LOG2_INSHIFT))
#define OD_LOG2_OUTSCALE (1 << OD_LOG2_OUTSHIFT)
static int16_t od_log2(int16_t x)
{
return x + OD_MULT16_16_Q15(x, (14482 + OD_MULT16_16_Q15(x, (-23234
+ OD_MULT16_16_Q15(x, (13643 + OD_MULT16_16_Q15(x, (-6403
+ OD_MULT16_16_Q15(x, 1515)))))))));
}
static int32_t od_pow(int32_t x, od_val16 beta)
{
int16_t t;
int xshift;
int log2_x;
od_val32 logr;
/*FIXME: this conditional is to avoid doing log2(0).*/
if (x == 0)
return 0;
log2_x = (OD_ILOG(x) - 1);
xshift = log2_x - OD_LOG2_INSHIFT;
/*t should be in range [0.0, 1.0[ in Q(OD_LOG2_INSHIFT).*/
t = OD_VSHR(x, xshift) - (1 << OD_LOG2_INSHIFT);
/*log2(g/OD_COMPAND_SCALE) = log2(x) - OD_COMPAND_SHIFT in
Q(OD_LOG2_OUTSHIFT).*/
logr = od_log2(t) + (log2_x - OD_COMPAND_SHIFT)*OD_LOG2_OUTSCALE;
logr = OD_MULT16_32_QBETA(beta, logr);
return od_exp2(logr);
}
#endif
/** Gain companding: raises gain to the power 1/beta for activity masking.
*
* @param [in] g real (uncompanded) gain
* @param [in] q0 uncompanded quality parameter
* @param [in] beta activity masking beta param (exponent)
* @return g^(1/beta)
*/
static od_val32 od_gain_compand(od_val32 g, int q0, od_val16 beta) {
#if defined(OD_FLOAT_PVQ)
if (beta == 1) return OD_CGAIN_SCALE*g/(double)q0;
else {
return OD_CGAIN_SCALE*OD_COMPAND_SCALE*pow(g*OD_COMPAND_SCALE_1,
1./beta)/(double)q0;
}
#else
if (beta == OD_BETA(1)) return (OD_CGAIN_SCALE*g + (q0 >> 1))/q0;
else {
int32_t expr;
expr = od_pow(g, od_beta_rcp(beta));
expr <<= OD_CGAIN_SHIFT + OD_COMPAND_SHIFT - OD_EXP2_OUTSHIFT;
return (expr + (q0 >> 1))/q0;
}
#endif
}
#if !defined(OD_FLOAT_PVQ)
#define OD_SQRT_INSHIFT 16
#define OD_SQRT_OUTSHIFT 15
static int16_t od_rsqrt_norm(int16_t x);
static int16_t od_sqrt_norm(int32_t x)
{
OD_ASSERT(x < 65536);
return OD_MINI(OD_SHR_ROUND(x*od_rsqrt_norm(x), OD_SQRT_OUTSHIFT), 32767);
}
static int16_t od_sqrt(int32_t x, int *sqrt_shift)
{
int k;
int s;
int32_t t;
if (x == 0) {
*sqrt_shift = 0;
return 0;
}
OD_ASSERT(x < (1 << 30));
k = ((OD_ILOG(x) - 1) >> 1);
/*t is x in the range [0.25, 1) in QINSHIFT, or x*2^(-s).
Shift by log2(x) - log2(0.25*(1 << INSHIFT)) to ensure 0.25 lower bound.*/
s = 2*k - (OD_SQRT_INSHIFT - 2);
t = OD_VSHR(x, s);
/*We want to express od_sqrt() in terms of od_sqrt_norm(), which is
defined as (2^OUTSHIFT)*sqrt(t*(2^-INSHIFT)) with t=x*(2^-s).
This simplifies to 2^(OUTSHIFT-(INSHIFT/2)-(s/2))*sqrt(x), so the caller
needs to shift right by OUTSHIFT - INSHIFT/2 - s/2.*/
*sqrt_shift = OD_SQRT_OUTSHIFT - ((s + OD_SQRT_INSHIFT) >> 1);
return od_sqrt_norm(t);
}
#endif
/** Gain expanding: raises gain to the power beta for activity masking.
*
* @param [in] cg companded gain
* @param [in] q0 uncompanded quality parameter
* @param [in] beta activity masking beta param (exponent)
* @return g^beta
*/
od_val32 od_gain_expand(od_val32 cg0, int q0, od_val16 beta) {
if (beta == OD_BETA(1)) {
/*The multiply fits into 28 bits because the expanded gain has a range from
0 to 2^20.*/
return OD_SHR_ROUND(cg0*q0, OD_CGAIN_SHIFT);
}
else if (beta == OD_BETA(1.5)) {
#if defined(OD_FLOAT_PVQ)
double cg;
cg = cg0*OD_CGAIN_SCALE_1;
cg *= q0*OD_COMPAND_SCALE_1;
return OD_COMPAND_SCALE*cg*sqrt(cg);
#else
int32_t irt;
int64_t tmp;
int sqrt_inshift;
int sqrt_outshift;
/*cg0 is in Q(OD_CGAIN_SHIFT) and we need to divide it by
2^OD_COMPAND_SHIFT.*/
irt = od_sqrt(cg0*q0, &sqrt_outshift);
sqrt_inshift = (OD_CGAIN_SHIFT + OD_COMPAND_SHIFT) >> 1;
/*tmp is in Q(OD_CGAIN_SHIFT + OD_COMPAND_SHIFT).*/
tmp = cg0*q0*(int64_t)irt;
/*Expanded gain must be in Q(OD_COMPAND_SHIFT), thus OD_COMPAND_SHIFT is
not included here.*/
return OD_MAXI(1,
OD_VSHR_ROUND(tmp, OD_CGAIN_SHIFT + sqrt_outshift + sqrt_inshift));
#endif
}
else {
#if defined(OD_FLOAT_PVQ)
/*Expanded gain must be in Q(OD_COMPAND_SHIFT), hence the multiply by
OD_COMPAND_SCALE.*/
double cg;
cg = cg0*OD_CGAIN_SCALE_1;
return OD_COMPAND_SCALE*pow(cg*q0*OD_COMPAND_SCALE_1, beta);
#else
int32_t expr;
int32_t cg;
cg = OD_SHR_ROUND(cg0*q0, OD_CGAIN_SHIFT);
expr = od_pow(cg, beta);
/*Expanded gain must be in Q(OD_COMPAND_SHIFT), hence the subtraction by
OD_COMPAND_SHIFT.*/
return OD_MAXI(1, OD_SHR_ROUND(expr, OD_EXP2_OUTSHIFT - OD_COMPAND_SHIFT));
#endif
}
}
/** Computes the raw and quantized/companded gain of a given input
* vector
*
* @param [in] x vector of input data
* @param [in] n number of elements in vector x
* @param [in] q0 quantizer
* @param [out] g raw gain
* @param [in] beta activity masking beta param
* @param [in] bshift shift to be applied to raw gain
* @return quantized/companded gain
*/
od_val32 od_pvq_compute_gain(const od_val16 *x, int n, int q0, od_val32 *g,
od_val16 beta, int bshift) {
int i;
od_val32 acc;
#if !defined(OD_FLOAT_PVQ)
od_val32 irt;
int sqrt_shift;
#else
OD_UNUSED(bshift);
#endif
acc = 0;
for (i = 0; i < n; i++) {
acc += x[i]*(od_val32)x[i];
}
#if defined(OD_FLOAT_PVQ)
*g = sqrt(acc);
#else
irt = od_sqrt(acc, &sqrt_shift);
*g = OD_VSHR_ROUND(irt, sqrt_shift - bshift);
#endif
/* Normalize gain by quantization step size and apply companding
(if ACTIVITY != 1). */
return od_gain_compand(*g, q0, beta);
}
/** Compute theta quantization range from quantized/companded gain
*
* @param [in] qcg quantized companded gain value
* @param [in] beta activity masking beta param
* @return max theta value
*/
int od_pvq_compute_max_theta(od_val32 qcg, od_val16 beta){
/* Set angular resolution (in ra) to match the encoded gain */
#if defined(OD_FLOAT_PVQ)
int ts = (int)floor(.5 + qcg*OD_CGAIN_SCALE_1*M_PI/(2*beta));
#else
int ts = OD_SHR_ROUND(qcg*OD_MULT16_16_QBETA(OD_QCONST32(M_PI/2,
OD_CGAIN_SHIFT), od_beta_rcp(beta)), OD_CGAIN_SHIFT*2);
#endif
/* Special case for low gains -- will need to be tuned anyway */
if (qcg < OD_QCONST32(1.4, OD_CGAIN_SHIFT)) ts = 1;
return ts;
}
/** Decode quantized theta value from coded value
*
* @param [in] t quantized companded gain value
* @param [in] max_theta maximum theta value
* @return decoded theta value
*/
od_val32 od_pvq_compute_theta(int t, int max_theta) {
if (max_theta != 0) {
#if defined(OD_FLOAT_PVQ)
return OD_MINI(t, max_theta - 1)*.5*M_PI/max_theta;
#else
return (OD_MAX_THETA_SCALE*OD_MINI(t, max_theta - 1)
+ (max_theta >> 1))/max_theta;
#endif
}
else return 0;
}
#define OD_SQRT_TBL_SHIFT (10)
#define OD_ITHETA_SHIFT 15
/** Compute the number of pulses used for PVQ encoding a vector from
* available metrics (encode and decode side)
*
* @param [in] qcg quantized companded gain value
* @param [in] itheta quantized PVQ error angle theta
* @param [in] noref indicates present or lack of reference
* (prediction)
* @param [in] n number of elements to be coded
* @param [in] beta activity masking beta param
* @return number of pulses to use for coding
*/
int od_pvq_compute_k(od_val32 qcg, int itheta, int noref, int n,
od_val16 beta) {
#if !defined(OD_FLOAT_PVQ)
/*Lookup table for sqrt(n+3/2) and sqrt(n+2/2) in Q10.
Real max values are 32792 and 32784, but clamped to stay within 16 bits.
Update with tools/gen_sqrt_tbl if needed.*/
static const od_val16 od_sqrt_table[2][13] = {
{0, 0, 0, 0, 2290, 2985, 4222, 0, 8256, 0, 16416, 0, 32767},
{0, 0, 0, 0, 2401, 3072, 4284, 0, 8287, 0, 16432, 0, 32767}};
#endif
if (noref) {
if (qcg == 0) return 0;
if (n == 15 && qcg == OD_CGAIN_SCALE && beta > OD_BETA(1.25)) {
return 1;
}
else {
#if defined(OD_FLOAT_PVQ)
return OD_MAXI(1, (int)floor(.5 + (qcg*OD_CGAIN_SCALE_1 - .2)*
sqrt((n + 3)/2)/beta));
#else
od_val16 rt;
OD_ASSERT(OD_ILOG(n + 1) < 13);
rt = od_sqrt_table[1][OD_ILOG(n + 1)];
/*FIXME: get rid of 64-bit mul.*/
return OD_MAXI(1, OD_SHR_ROUND((int64_t)((qcg
- (int64_t)OD_QCONST32(.2, OD_CGAIN_SHIFT))*
OD_MULT16_16_QBETA(od_beta_rcp(beta), rt)), OD_CGAIN_SHIFT
+ OD_SQRT_TBL_SHIFT));
#endif
}
}
else {
if (itheta == 0) return 0;
/* Sets K according to gain and theta, based on the high-rate
PVQ distortion curves (see PVQ document). Low-rate will have to be
perceptually tuned anyway. We subtract 0.2 from the radius as an
approximation for the fact that the coefficients aren't identically
distributed within a band so at low gain the number of dimensions that
are likely to have a pulse is less than n. */
#if defined(OD_FLOAT_PVQ)
return OD_MAXI(1, (int)floor(.5 + (itheta - .2)*sqrt((n + 2)/2)));
#else
od_val16 rt;
OD_ASSERT(OD_ILOG(n + 1) < 13);
rt = od_sqrt_table[0][OD_ILOG(n + 1)];
/*FIXME: get rid of 64-bit mul.*/
return OD_MAXI(1, OD_VSHR_ROUND(((OD_SHL(itheta, OD_ITHETA_SHIFT)
- OD_QCONST32(.2, OD_ITHETA_SHIFT)))*(int64_t)rt,
OD_SQRT_TBL_SHIFT + OD_ITHETA_SHIFT));
#endif
}
}
#if !defined(OD_FLOAT_PVQ)
#define OD_RSQRT_INSHIFT 16
#define OD_RSQRT_OUTSHIFT 14
/** Reciprocal sqrt approximation where the input is in the range [0.25,1) in
Q16 and the output is in the range (1.0, 2.0] in Q14).
Error is always within +/1 of round(1/sqrt(t))*/
static int16_t od_rsqrt_norm(int16_t t)
{
int16_t n;
int32_t r;
int32_t r2;
int32_t ry;
int32_t y;
int32_t ret;
/* Range of n is [-16384,32767] ([-0.5,1) in Q15).*/
n = t - 32768;
OD_ASSERT(n >= -16384);
/*Get a rough initial guess for the root.
The optimal minimax quadratic approximation (using relative error) is
r = 1.437799046117536+n*(-0.823394375837328+n*0.4096419668459485).
Coefficients here, and the final result r, are Q14.*/
r = (23565 + OD_MULT16_16_Q15(n, (-13481 + OD_MULT16_16_Q15(n, 6711))));
/*We want y = t*r*r-1 in Q15, but t is 32-bit Q16 and r is Q14.
We can compute the result from n and r using Q15 multiplies with some
adjustment, carefully done to avoid overflow.*/
r2 = r*r;
y = (((r2 >> 15)*n + r2) >> 12) - 131077;
ry = r*y;
/*Apply a 2nd-order Householder iteration: r += r*y*(y*0.375-0.5).
This yields the Q14 reciprocal square root of the Q16 t, with a maximum
relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a peak
absolute error of 2.26591/16384.*/
ret = r + ((((ry >> 16)*(3*y) >> 3) - ry) >> 18);
OD_ASSERT(ret >= 16384 && ret < 32768);
return (int16_t)ret;
}
static int16_t od_rsqrt(int32_t x, int *rsqrt_shift)
{
int k;
int s;
int16_t t;
k = (OD_ILOG(x) - 1) >> 1;
/*t is x in the range [0.25, 1) in QINSHIFT, or x*2^(-s).
Shift by log2(x) - log2(0.25*(1 << INSHIFT)) to ensure 0.25 lower bound.*/
s = 2*k - (OD_RSQRT_INSHIFT - 2);
t = OD_VSHR(x, s);
/*We want to express od_rsqrt() in terms of od_rsqrt_norm(), which is
defined as (2^OUTSHIFT)/sqrt(t*(2^-INSHIFT)) with t=x*(2^-s).
This simplifies to 2^(OUTSHIFT+(INSHIFT/2)+(s/2))/sqrt(x), so the caller
needs to shift right by OUTSHIFT + INSHIFT/2 + s/2.*/
*rsqrt_shift = OD_RSQRT_OUTSHIFT + ((s + OD_RSQRT_INSHIFT) >> 1);
return od_rsqrt_norm(t);
}
#endif
/** Synthesizes one parition of coefficient values from a PVQ-encoded
* vector. This 'partial' version is called by the encode loop where
* the Householder reflection has already been computed and there's no
* need to recompute it.
*
* @param [out] xcoeff output coefficient partition (x in math doc)
* @param [in] ypulse PVQ-encoded values (y in the math doc); in
* the noref case, this vector has n entries,
* in the reference case it contains n-1 entries
* (the m-th entry is not included)
* @param [in] r reference vector (prediction)
* @param [in] n number of elements in this partition
* @param [in] noref indicates presence or lack of prediction
* @param [in] g decoded quantized vector gain
* @param [in] theta decoded theta (prediction error)
* @param [in] m alignment dimension of Householder reflection
* @param [in] s sign of Householder reflection
* @param [in] qm_inv inverse of the QM with magnitude compensation
*/
void od_pvq_synthesis_partial(od_coeff *xcoeff, const od_coeff *ypulse,
const od_val16 *r16, int n, int noref, od_val32 g, od_val32 theta, int m, int s,
const int16_t *qm_inv) {
int i;
int yy;
od_val32 scale;
int nn;
#if !defined(OD_FLOAT_PVQ)
int gshift;
int qshift;
#endif
OD_ASSERT(g != 0);
nn = n-(!noref); /* when noref==0, vector in is sized n-1 */
yy = 0;
for (i = 0; i < nn; i++)
yy += ypulse[i]*(int32_t)ypulse[i];
#if !defined(OD_FLOAT_PVQ)
/* Shift required for the magnitude of the pre-qm synthesis to be guaranteed
to fit in 16 bits. In practice, the range will be 8192-16384 after scaling
most of the time. */
gshift = OD_MAXI(0, OD_ILOG(g) - 14);
#endif
/*scale is g/sqrt(yy) in Q(16-gshift) so that x[]*scale has a norm that fits
in 16 bits.*/
if (yy == 0) scale = 0;
#if defined(OD_FLOAT_PVQ)
else {
scale = g/sqrt(yy);
}
#else
else {
int rsqrt_shift;
int16_t rsqrt;
/*FIXME: should be < int64_t*/
int64_t tmp;
rsqrt = od_rsqrt(yy, &rsqrt_shift);
tmp = rsqrt*(int64_t)g;
scale = OD_VSHR_ROUND(tmp, rsqrt_shift + gshift - 16);
}
/* Shift to apply after multiplying by the inverse QM, taking into account
gshift. */
qshift = OD_QM_INV_SHIFT - gshift;
#endif
if (noref) {
for (i = 0; i < n; i++) {
od_val32 x;
/* This multiply doesn't round, so it introduces some bias.
It would be nice (but not critical) to fix this. */
x = OD_MULT16_32_Q16(ypulse[i], scale);
#if defined(OD_FLOAT_PVQ)
xcoeff[i] = (od_coeff)floor(.5
+ x*(qm_inv[i]*OD_QM_INV_SCALE_1));
#else
xcoeff[i] = OD_SHR_ROUND(x*qm_inv[i], qshift);
#endif
}
}
else{
od_val16 x[MAXN];
scale = OD_ROUND32(scale*OD_TRIG_SCALE_1*od_pvq_sin(theta));
/* The following multiply doesn't round, but it's probably OK since
the Householder reflection is likely to undo most of the resulting
bias. */
for (i = 0; i < m; i++)
x[i] = OD_MULT16_32_Q16(ypulse[i], scale);
x[m] = OD_ROUND16(-s*(OD_SHR_ROUND(g, gshift))*OD_TRIG_SCALE_1*
od_pvq_cos(theta));
for (i = m; i < nn; i++)
x[i+1] = OD_MULT16_32_Q16(ypulse[i], scale);
od_apply_householder(x, x, r16, n);
for (i = 0; i < n; i++) {
#if defined(OD_FLOAT_PVQ)
xcoeff[i] = (od_coeff)floor(.5 + (x[i]*(qm_inv[i]*OD_QM_INV_SCALE_1)));
#else
xcoeff[i] = OD_SHR_ROUND(x[i]*qm_inv[i], qshift);
#endif
}
}
}