uvg266/src/intra.c

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/*****************************************************************************
* This file is part of Kvazaar HEVC encoder.
*
* Copyright (C) 2013-2014 Tampere University of Technology and others (see
* COPYING file).
*
* Kvazaar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as published
* by the Free Software Foundation.
*
* Kvazaar 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Kvazaar. If not, see <http://www.gnu.org/licenses/>.
****************************************************************************/
/**
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* \file
* \brief Functions for handling intra frames.
*/
#include "intra.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "config.h"
#include "encoder.h"
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const uint8_t intra_hor_ver_dist_thres[5] = {0,7,1,0,0};
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/**
* \brief Set intrablock mode (and init typedata)
* \param pic picture to use
* \param xCtb x CU position (smallest CU)
* \param yCtb y CU position (smallest CU)
* \param depth current CU depth
* \param mode mode to set
* \returns Void
*/
void intra_set_block_mode(picture *pic,uint32_t x_cu, uint32_t y_cu, uint8_t depth, uint8_t mode)
{
uint32_t x, y;
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int width_in_scu = pic->width_in_lcu<<MAX_DEPTH; //!< Width in smallest CU
int block_scu_width = (LCU_WIDTH>>depth)/(LCU_WIDTH>>MAX_DEPTH);
// Loop through all the blocks in the area of cur_cu
for (y = y_cu; y < y_cu + block_scu_width; y++) {
int cu_pos = y * width_in_scu;
for (x = x_cu; x < x_cu + block_scu_width; x++) {
pic->cu_array[MAX_DEPTH][cu_pos + x].depth = depth;
pic->cu_array[MAX_DEPTH][cu_pos + x].type = CU_INTRA;
pic->cu_array[MAX_DEPTH][cu_pos + x].intra.mode = mode;
}
}
}
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/**
* \brief get intrablock mode
* \param pic picture to use
* \param xCtb x CU position (smallest CU)
* \param yCtb y CU position (smallest CU)
* \param depth current CU depth
* \returns mode if it's present, otherwise -1
*/
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int8_t intra_get_block_mode(picture *pic, uint32_t x_cu, uint32_t y_cu, uint8_t depth)
{
int width_in_scu = pic->width_in_lcu<<MAX_DEPTH; //!< width in smallest CU
int cu_pos = y_cu * width_in_scu + x_cu;
if (pic->cu_array[MAX_DEPTH][cu_pos].type == CU_INTRA) {
return pic->cu_array[MAX_DEPTH][cu_pos].intra.mode;
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}
return -1;
}
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/**
* \brief get intrablock mode
* \param pic picture data to use
* \param picwidth width of the picture data
* \param xpos x-position
* \param ypos y-position
* \param width block width
* \returns DC prediction
*/
int16_t intra_get_dc_pred(pixel *pic, uint16_t picwidth, uint32_t xpos, uint32_t ypos, uint8_t width)
{
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int32_t i, sum = 0;
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// pixels on top and left
for (i = -picwidth; i < width - picwidth; i++) {
sum += pic[i];
}
for (i = -1; i < width * picwidth - 1; i += picwidth) {
sum += pic[i];
}
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// return the average
return (sum + width) / (width + width);
}
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/**
* \brief Function for deriving intra luma predictions
* \param pic picture to use
* \param x_cu x CU position (smallest CU)
* \param y_cu y CU position (smallest CU)
* \param depth current CU depth
* \param preds output buffer for 3 predictions
* \returns (predictions are found)?1:0
*/
int8_t intra_get_dir_luma_predictor(picture* pic, uint32_t x_cu, uint32_t y_cu, uint8_t depth, int8_t* preds)
{
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int32_t left_intra_dir = 1; // reset to DC_IDX
int32_t above_intra_dir = 1; // reset to DC_IDX
int width_in_scu = pic->width_in_lcu<<MAX_DEPTH;
int32_t cu_pos = y_cu * width_in_scu + x_cu;
// Left PU predictor
if(x_cu && pic->cu_array[MAX_DEPTH][cu_pos - 1].type == CU_INTRA && pic->cu_array[MAX_DEPTH][cu_pos - 1].coded) {
left_intra_dir = pic->cu_array[MAX_DEPTH][cu_pos - 1].intra.mode;
}
// Top PU predictor
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if(y_cu && ((y_cu * (LCU_WIDTH>>MAX_DEPTH)) % LCU_WIDTH) != 0
&& pic->cu_array[MAX_DEPTH][cu_pos - width_in_scu].type == CU_INTRA && pic->cu_array[MAX_DEPTH][cu_pos - width_in_scu].coded) {
above_intra_dir = pic->cu_array[MAX_DEPTH][cu_pos - width_in_scu].intra.mode;
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}
// If the predictions are the same, add new predictions
if (left_intra_dir == above_intra_dir) {
if (left_intra_dir > 1) { // angular modes
preds[0] = left_intra_dir;
preds[1] = ((left_intra_dir + 29) % 32) + 2;
preds[2] = ((left_intra_dir - 1 ) % 32) + 2;
} else { //non-angular
preds[0] = 0;//PLANAR_IDX;
preds[1] = 1;//DC_IDX;
preds[2] = 26;//VER_IDX;
}
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} else { // If we have two distinct predictions
preds[0] = left_intra_dir;
preds[1] = above_intra_dir;
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// add planar mode if it's not yet present
if (left_intra_dir && above_intra_dir ) {
preds[2] = 0; // PLANAR_IDX;
} else { // else we add 26 or 1
preds[2] = (left_intra_dir+above_intra_dir)<2? 26 : 1;
}
}
return 1;
}
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/**
* \brief Intra filtering of the border samples
* \param ref reference picture data
* \param x_cu x CU position (smallest CU)
* \param y_cu y CU position (smallest CU)
* \param depth current CU depth
* \param preds output buffer for 3 predictions
* \returns (predictions are found)?1:0
*/
void intra_filter(pixel *ref, int32_t stride,int32_t width, int8_t mode)
{
#define FWIDTH (LCU_WIDTH*2+1)
pixel filtered[FWIDTH * FWIDTH]; //!< temporary buffer for filtered samples
pixel *filteredShift = &filtered[FWIDTH+1]; //!< pointer to temporary buffer with offset (1,1)
int x,y;
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if (!mode) {
// pF[ -1 ][ -1 ] = ( p[ -1 ][ 0 ] + 2*p[ -1 ][ -1 ] + p[ 0 ][ -1 ] + 2 ) >> 2 (8 35)
filteredShift[-FWIDTH-1] = (ref[-1] + 2*ref[-(int32_t)stride-1] + ref[-(int32_t)stride] + 2) >> 2;
// pF[ -1 ][ y ] = ( p[ -1 ][ y + 1 ] + 2*p[ -1 ][ y ] + p[ -1 ][ y - 1 ] + 2 ) >> 2 for y = 0..nTbS * 2 - 2 (8 36)
for (y = 0; y < (int32_t)width * 2 - 1; y++) {
filteredShift[y*FWIDTH-1] = (ref[(y + 1) * stride - 1] + 2*ref[y * stride - 1] + ref[(y - 1) * stride - 1] + 2) >> 2;
}
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// pF[ -1 ][ nTbS * 2 - 1 ] = p[ -1 ][ nTbS * 2 - 1 ] (8 37)
filteredShift[(width * 2 - 1) * FWIDTH - 1] = ref[(width * 2 - 1) * stride - 1];
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// pF[ x ][ -1 ] = ( p[ x - 1 ][ -1 ] + 2*p[ x ][ -1 ] + p[ x + 1 ][ -1 ] + 2 ) >> 2 for x = 0..nTbS * 2 - 2 (8 38)
for(x = 0; x < (int32_t)width*2-1; x++) {
filteredShift[x - FWIDTH] = (ref[x - 1 - stride] + 2*ref[x - stride] + ref[x + 1 - stride] + 2) >> 2;
}
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// pF[ nTbS * 2 - 1 ][ -1 ] = p[ nTbS * 2 - 1 ][ -1 ]
filteredShift[(width * 2 - 1) - FWIDTH] = ref[(width * 2 - 1) - stride];
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// Copy filtered samples to the input array
for (x = -1; x < (int32_t)width * 2; x++) {
ref[x - stride] = filtered[x + 1];
}
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for(y = 0; y < (int32_t)width * 2; y++) {
ref[y * stride - 1] = filtered[(y + 1) * FWIDTH];
}
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} else {
printf("UNHANDLED: %s: %d\r\n", __FILE__, __LINE__);
exit(1);
}
#undef FWIDTH
}
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/**
* \brief Function to test best intra prediction mode
* \param orig original picture data
* \param origstride original picture stride
* \param rec reconstructed picture data
* \param recstride reconstructed picture stride
* \param xpos source x-position
* \param ypos source y-position
* \param width block size to predict
* \param dst destination buffer for best prediction
* \param dststride destination width
* \param sad_out sad value of best mode
* \returns best intra mode
This function derives the prediction samples for planar mode (intra coding).
*/
int16_t intra_prediction(pixel *orig, int32_t origstride, pixel *rec, int32_t recstride, uint32_t xpos,
uint32_t ypos, uint32_t width, pixel *dst, int32_t dststride, uint32_t *sad_out)
{
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uint32_t best_sad = 0xffffffff;
uint32_t sad = 0;
int16_t best_mode = 1;
int32_t x,y,i;
cost_16bit_nxn_func cost_func = get_sad_16bit_nxn_func(width);
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// Temporary block arrays
// TODO: alloc with alignment
pixel pred[LCU_WIDTH * LCU_WIDTH + 1];
pixel orig_block[LCU_WIDTH * LCU_WIDTH + 1];
pixel rec_filtered_temp[(LCU_WIDTH * 2 + 8) * (LCU_WIDTH * 2 + 8) + 1];
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pixel* rec_filtered = &rec_filtered_temp[recstride + 1]; //!< pointer to rec_filtered_temp with offset of (1,1)
pixel *orig_shift = &orig[xpos + ypos*origstride]; //!< pointer to orig with offset of (1,1)
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int8_t filter = (width<32); // TODO: chroma support
uint8_t threshold = intra_hor_ver_dist_thres[g_to_bits[width]]; //!< Intra filtering threshold
#define COPY_PRED_TO_DST() for (y = 0; y < (int32_t)width; y++) { for (x = 0; x < (int32_t)width; x++) { dst[x + y*dststride] = pred[x + y*width]; } }
#define CHECK_FOR_BEST(mode, additional_sad) sad = cost_func(pred, orig_block); \
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sad += additional_sad;\
if(sad < best_sad)\
{\
best_sad = sad;\
best_mode = mode;\
COPY_PRED_TO_DST();\
}
// Store original block for SAD computation
i = 0;
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for(y = 0; y < (int32_t)width; y++) {
for(x = 0; x < (int32_t)width; x++) {
orig_block[i++] = orig_shift[x + y*origstride];
}
}
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// Filtered only needs the borders
for (y = -1; y < (int32_t)recstride; y++) {
rec_filtered[y*recstride - 1] = rec[y*recstride - 1];
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}
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for (x = 0; x < (int32_t)recstride; x++) {
rec_filtered[y - recstride] = rec[y - recstride];
}
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// Apply filter
intra_filter(rec_filtered,recstride,width,0);
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// Test DC mode (never filtered)
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x = intra_get_dc_pred(rec, recstride, xpos, ypos, width);
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for (i = 0; i < (int32_t)(width*width); i++) {
pred[i] = x;
}
CHECK_FOR_BEST(1,0);
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// Check angular not requiring filtering
for (i = 2; i < 35; i++) {
int distance = MIN(abs(i - 26),abs(i - 10)); //!< Distance from top and left predictions
if(distance <= threshold) {
intra_get_angular_pred(rec, recstride, pred, width, width, width, i, xpos?1:0, ypos?1:0, filter);
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CHECK_FOR_BEST(i,0);
}
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}
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// FROM THIS POINT FORWARD, USING FILTERED PREDICTION
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// Test planar mode (always filtered)
intra_get_planar_pred(rec_filtered, recstride, xpos, ypos, width, pred, width);
CHECK_FOR_BEST(0,0);
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// Check angular predictions which require filtered samples
// TODO: add conditions to skip some modes on borders
// chroma can use only 26 and 10 (if not using luma-prediction)
for (i = 2; i < 35; i++) {
int distance = MIN(abs(i-26),abs(i-10)); //!< Distance from top and left predictions
if(distance > threshold) {
intra_get_angular_pred(rec_filtered, recstride, pred, width, width, width, i, xpos?1:0, ypos?1:0, filter);
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CHECK_FOR_BEST(i,0);
}
}
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// assign final sad to output
*sad_out = best_sad;
#undef COPY_PRED_TO_DST
#undef CHECK_FOR_BEST
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return best_mode;
}
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/**
* \brief Reconstruct intra block according to prediction
* \param rec reconstructed picture data
* \param recstride reconstructed picture stride
* \param xpos source x-position
* \param ypos source y-position
* \param width block size to predict
* \param dst destination buffer for best prediction
* \param dststride destination width
* \param mode intra mode to use
* \param chroma chroma-block flag
*/
void intra_recon(pixel* rec,uint32_t recstride, uint32_t xpos, uint32_t ypos,uint32_t width, pixel* dst,int32_t dststride, int8_t mode, int8_t chroma)
{
int32_t x,y,i;
pixel pred[LCU_WIDTH * LCU_WIDTH];
int8_t filter = !chroma&&(width<32);
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#define COPY_PRED_TO_DST() for(y = 0; y < (int32_t)width; y++) { for(x = 0; x < (int32_t)width; x++) { dst[x+y*dststride] = pred[x+y*width]; } }
// Filtering apply if luma and not DC
if (!chroma && mode != 1) {
uint8_t threshold = intra_hor_ver_dist_thres[g_to_bits[width]];
if(MIN(abs(mode-26),abs(mode-10)) > threshold) {
intra_filter(rec,recstride,width,0);
}
}
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// planar
if (mode == 0) {
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intra_get_planar_pred(rec, recstride, xpos, ypos, width, pred, width);
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} else if (mode == 1) { // DC
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i = intra_get_dc_pred(rec, recstride, xpos, ypos, width);
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for (y = 0; y < (int32_t)width; y++) {
for (x = 0; x < (int32_t)width; x++) {
dst[x + y*dststride] = i;
}
}
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// Assigned value directly to output, no need to stay here
return;
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} else { // directional predictions
intra_get_angular_pred(rec, recstride,pred, width, width, width, mode, xpos?1:0, ypos?1:0, filter);
}
COPY_PRED_TO_DST();
#undef COPY_PRED_TO_DST
}
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/**
* \brief this functions build a reference block (only borders) used for intra predictions
* \param pic picture to use as a source, should contain full CU-data
* \param outwidth width of the prediction block
* \param chroma signaling if chroma is used, 0 = luma, 1 = U and 2 = V
*
*/
void intra_build_reference_border(picture *pic, int32_t x_cu, int32_t y_cu,int16_t outwidth, pixel *dst, int32_t dststride, int8_t chroma)
{
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int32_t left_column; //!< left column iterator
pixel val; //!< variable to store extrapolated value
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int32_t i; //!< index iterator
pixel dc_val = 1<<(g_bitdepth-1); //!< default predictor value
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int32_t top_row; //!< top row iterator
int32_t src_width = (pic->width>>(chroma?1:0)); //!< source picture width
int32_t src_height = (pic->height>>(chroma?1:0));//!< source picture height
pixel *src = (!chroma) ? pic->y_recdata : ((chroma == 1) ? pic->u_recdata : pic->v_recdata); //!< input picture pointer
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int16_t scu_width = LCU_WIDTH>>(MAX_DEPTH+(chroma?1:0)); //!< Smallest Coding Unit width
pixel *src_shifted = &src[x_cu * scu_width + (y_cu * scu_width) * src_width]; //!< input picture pointer shifted to start from the left-top corner of the current block
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int width_in_scu = pic->width_in_lcu<<MAX_DEPTH; //!< picture width in smallest CU
// Fill left column when not on the border
if (x_cu) {
// loop SCU's
for (left_column = 1; left_column < outwidth / scu_width; left_column++) {
// If over the picture height or block not yet coded, stop
if ((y_cu + left_column) * scu_width >= src_height || !pic->cu_array[MAX_DEPTH][x_cu - 1 + (y_cu + left_column) * width_in_scu].coded) {
break;
}
}
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// Copy the pixels to output
for (i = 0; i < left_column*scu_width - 1; i ++) {
dst[(i + 1) * dststride] = src_shifted[i*src_width - 1];
}
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// if the loop was not completed, extrapolate the last pixel pushed to output
if (left_column != outwidth / scu_width) {
val = src_shifted[(left_column * scu_width - 1) * src_width - 1];
for(i = (left_column * scu_width); i < outwidth; i++) {
dst[i * dststride] = val;
}
}
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} else { // If left column not available, copy from toprow or use the default predictor
val = y_cu ? src_shifted[-src_width] : dc_val;
for (i = 0; i < outwidth; i++) {
dst[i * dststride] = val;
}
}
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if(y_cu) {
// Loop top SCU's
for(top_row = 1; top_row < outwidth / scu_width; top_row++) {
// If over the picture width or block not yet coded, stop
if ((x_cu + top_row) * scu_width >= src_width || !pic->cu_array[MAX_DEPTH][x_cu + top_row+(y_cu - 1) * width_in_scu].coded) {
break;
}
}
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// Copy the pixels to output
for(i = 0; i < top_row * scu_width - 1; i++) {
dst[i + 1] = src_shifted[i - src_width];
}
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if(top_row != outwidth/scu_width) {
val = src_shifted[(top_row * scu_width) - src_width - 1];
for(i = (top_row * scu_width); i < outwidth; i++) {
dst[i] = val;
}
}
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} else {
val = x_cu ? src_shifted[-1] : dc_val;
for(i = 1; i < outwidth; i++)
{
dst[i] = val;
}
}
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// Topleft corner sample
dst[0] = (x_cu && y_cu) ? src_shifted[-src_width - 1] : dst[dststride];
}
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const int32_t ang_table[9] = {0, 2, 5, 9, 13, 17, 21, 26, 32};
const int32_t inv_ang_table[9] = {0, 4096, 1638, 910, 630, 482, 390, 315, 256}; // (256 * 32) / Angle
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/**
* \brief this functions constructs the angular intra prediction from border samples
*
*/
void intra_get_angular_pred(pixel* src, int32_t src_stride, pixel* dst, int32_t dst_stride, int32_t width,
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int32_t height, int32_t dir_mode, int8_t left_avail,int8_t top_avail, int8_t filter)
{
int32_t k,l;
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int32_t blk_size = width;
// Map the mode index to main prediction direction and angle
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int8_t mode_hor = dir_mode < 18;
int8_t mode_ver = !mode_hor;
int32_t intra_pred_angle = mode_ver ? (int32_t)dir_mode - 26 : mode_hor ? -((int32_t)dir_mode - 10) : 0;
int32_t abs_ang = abs(intra_pred_angle);
int32_t sign_ang = intra_pred_angle < 0 ? -1 : 1;
// Set bitshifts and scale the angle parameter to block size
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int32_t inv_angle = inv_ang_table[abs_ang];
// Do angular predictions
pixel *ref_main;
pixel *ref_side;
pixel ref_above[2 * LCU_WIDTH + 1];
pixel ref_left[2 * LCU_WIDTH + 1];
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abs_ang = ang_table[abs_ang];
intra_pred_angle = sign_ang * abs_ang;
// Initialise the Main and Left reference array.
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if (intra_pred_angle < 0) {
int32_t invAngleSum = 128; // rounding for (shift by 8)
for (k = 0; k < blk_size + 1; k++) {
ref_above[k + blk_size - 1] = src[k - src_stride - 1];
ref_left[k + blk_size - 1] = src[(k - 1) * src_stride - 1];
}
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ref_main = (mode_ver ? ref_above : ref_left) + (blk_size - 1);
ref_side = (mode_ver ? ref_left : ref_above) + (blk_size - 1);
// Extend the Main reference to the left.
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for (k =- 1; k > blk_size * intra_pred_angle>>5; k--) {
invAngleSum += inv_angle;
ref_main[k] = ref_side[invAngleSum>>8];
}
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} else {
for (k = 0; k < 2 * blk_size + 1; k++) {
ref_above[k] = src[k - src_stride - 1];
ref_left[k] = src[(k - 1) * src_stride - 1];
}
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ref_main = mode_ver ? ref_above : ref_left;
ref_side = mode_ver ? ref_left : ref_above;
}
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if (intra_pred_angle == 0) {
for (k = 0; k < blk_size; k++) {
for (l = 0; l < blk_size; l++) {
dst[k * dst_stride + l] = ref_main[l + 1];
}
}
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if (filter) {
for (k=0;k<blk_size;k++) {
dst[k * dst_stride] = CLIP(0, (1<<g_bitdepth) - 1, dst[k * dst_stride] + (( ref_side[k + 1] - ref_side[0]) >> 1));
}
}
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} else {
int32_t delta_pos=0;
int32_t delta_int;
int32_t delta_fract;
int32_t minus_delta_fract;
int32_t ref_main_index;
for (k = 0; k < blk_size; k++) {
delta_pos += intra_pred_angle;
delta_int = delta_pos >> 5;
delta_fract = delta_pos & (32 - 1);
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if (delta_fract) {
minus_delta_fract = (32 - delta_fract);
// Do linear filtering
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for (l = 0; l < blk_size; l++) {
ref_main_index = l + delta_int + 1;
dst[k * dst_stride + l] = (pixel) ( (minus_delta_fract * ref_main[ref_main_index]
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+ delta_fract * ref_main[ref_main_index + 1] + 16) >> 5);
}
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} else {
// Just copy the integer samples
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for (l = 0; l < blk_size; l++) {
dst[k * dst_stride + l] = ref_main[l + delta_int + 1];
}
}
}
}
// Flip the block if this is the horizontal mode
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if (mode_hor) {
pixel tmp;
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for (k=0;k<blk_size-1;k++) {
for (l=k+1;l<blk_size;l++) {
tmp = dst[k * dst_stride + l];
dst[k * dst_stride + l] = dst[l * dst_stride + k];
dst[l * dst_stride + k] = tmp;
}
}
}
}
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void intra_dc_pred_filtering(pixel *src, int32_t src_stride, pixel *dst, int32_t dst_stride, int32_t width, int32_t height )
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{
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int32_t x, y, dst_stride2, src_stride2;
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// boundary pixels processing
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dst[0] = ((src[-src_stride] + src[-1] + 2 * dst[0] + 2) >> 2);
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for (x = 1; x < width; x++) {
dst[x] = ((src[x - src_stride] + 3 * dst[x] + 2) >> 2);
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}
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for ( y = 1, dst_stride2 = dst_stride, src_stride2 = src_stride-1;
y < height; y++, dst_stride2+=dst_stride, src_stride2+=src_stride ) {
dst[dst_stride2] = ((src[src_stride2] + 3 * dst[dst_stride2] + 2) >> 2);
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}
return;
}
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/**
* \brief Function for deriving planar intra prediction.
* \param src source pixel array
* \param srcstride source width
* \param xpos source x-position
* \param ypos source y-position
* \param width block size to predict
* \param dst destination buffer for prediction
* \param dststride destination width
This function derives the prediction samples for planar mode (intra coding).
*/
void intra_get_planar_pred(pixel* src,int32_t srcstride, uint32_t xpos, uint32_t ypos,uint32_t width, pixel* dst,int32_t dststride)
{
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int32_t k, l, bottom_left, top_right;
int32_t hor_pred;
int32_t left_column[LCU_WIDTH+1], top_row[LCU_WIDTH+1], bottom_row[LCU_WIDTH+1], right_column[LCU_WIDTH+1];
uint32_t blk_size = width;
uint32_t offset_2d = width;
uint32_t shift_1d = g_convert_to_bit[ width ] + 2;
uint32_t shift_2d = shift_1d + 1;
// Get left and above reference column and row
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for (k = 0; k < (int32_t)blk_size + 1; k++) {
top_row[k] = src[k - srcstride];
left_column[k] = src[k * srcstride - 1];
}
// Prepare intermediate variables used in interpolation
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bottom_left = left_column[blk_size];
top_right = top_row[blk_size];
for (k = 0; k < (int32_t)blk_size; k++) {
bottom_row[k] = bottom_left - top_row[k];
right_column[k] = top_right - left_column[k];
top_row[k] <<= shift_1d;
left_column[k] <<= shift_1d;
}
// Generate prediction signal
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for (k = 0; k < (int32_t)blk_size; k++) {
hor_pred = left_column[k] + offset_2d;
for (l = 0; l < (int32_t)blk_size; l++) {
hor_pred += right_column[k];
top_row[l] += bottom_row[l];
dst[k * dststride + l] = ( (hor_pred + top_row[l]) >> shift_2d );
}
}
}