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rd.c
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rd.c
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/*
* Copyright (c) 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.
*/
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include "config/av1_rtcd.h"
#include "aom_dsp/aom_dsp_common.h"
#include "aom_mem/aom_mem.h"
#include "aom_ports/bitops.h"
#include "aom_ports/mem.h"
#include "aom_ports/system_state.h"
#include "av1/common/common.h"
#include "av1/common/entropy.h"
#include "av1/common/entropymode.h"
#include "av1/common/mvref_common.h"
#include "av1/common/pred_common.h"
#include "av1/common/quant_common.h"
#include "av1/common/reconinter.h"
#include "av1/common/reconintra.h"
#include "av1/common/seg_common.h"
#include "av1/encoder/av1_quantize.h"
#include "av1/encoder/cost.h"
#include "av1/encoder/encodemb.h"
#include "av1/encoder/encodemv.h"
#include "av1/encoder/encoder.h"
#include "av1/encoder/encodetxb.h"
#include "av1/encoder/mcomp.h"
#include "av1/encoder/ratectrl.h"
#include "av1/encoder/rd.h"
#include "av1/encoder/tokenize.h"
#define RD_THRESH_POW 1.25
// The baseline rd thresholds for breaking out of the rd loop for
// certain modes are assumed to be based on 8x8 blocks.
// This table is used to correct for block size.
// The factors here are << 2 (2 = x0.5, 32 = x8 etc).
static const uint8_t rd_thresh_block_size_factor[BLOCK_SIZES_ALL] = {
2, 3, 3, 4, 6, 6, 8, 12, 12, 16, 24, 24, 32, 48, 48, 64, 4, 4, 8, 8, 16, 16
};
static const int use_intra_ext_tx_for_txsize[EXT_TX_SETS_INTRA][EXT_TX_SIZES] =
{
{ 1, 1, 1, 1 }, // unused
{ 1, 1, 0, 0 },
{ 0, 0, 1, 0 },
};
static const int use_inter_ext_tx_for_txsize[EXT_TX_SETS_INTER][EXT_TX_SIZES] =
{
{ 1, 1, 1, 1 }, // unused
{ 1, 1, 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 1 },
};
static const int av1_ext_tx_set_idx_to_type[2][AOMMAX(EXT_TX_SETS_INTRA,
EXT_TX_SETS_INTER)] = {
{
// Intra
EXT_TX_SET_DCTONLY,
EXT_TX_SET_DTT4_IDTX_1DDCT,
EXT_TX_SET_DTT4_IDTX,
},
{
// Inter
EXT_TX_SET_DCTONLY,
EXT_TX_SET_ALL16,
EXT_TX_SET_DTT9_IDTX_1DDCT,
EXT_TX_SET_DCT_IDTX,
},
};
void av1_fill_mode_rates(AV1_COMMON *const cm, MACROBLOCK *x,
FRAME_CONTEXT *fc) {
int i, j;
for (i = 0; i < PARTITION_CONTEXTS; ++i)
av1_cost_tokens_from_cdf(x->partition_cost[i], fc->partition_cdf[i], NULL);
if (cm->skip_mode_flag) {
for (i = 0; i < SKIP_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->skip_mode_cost[i], fc->skip_mode_cdfs[i],
NULL);
}
}
for (i = 0; i < SKIP_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->skip_cost[i], fc->skip_cdfs[i], NULL);
}
for (i = 0; i < KF_MODE_CONTEXTS; ++i)
for (j = 0; j < KF_MODE_CONTEXTS; ++j)
av1_cost_tokens_from_cdf(x->y_mode_costs[i][j], fc->kf_y_cdf[i][j], NULL);
for (i = 0; i < BLOCK_SIZE_GROUPS; ++i)
av1_cost_tokens_from_cdf(x->mbmode_cost[i], fc->y_mode_cdf[i], NULL);
for (i = 0; i < CFL_ALLOWED_TYPES; ++i)
for (j = 0; j < INTRA_MODES; ++j)
av1_cost_tokens_from_cdf(x->intra_uv_mode_cost[i][j],
fc->uv_mode_cdf[i][j], NULL);
av1_cost_tokens_from_cdf(x->filter_intra_mode_cost, fc->filter_intra_mode_cdf,
NULL);
for (i = 0; i < BLOCK_SIZES_ALL; ++i) {
if (av1_filter_intra_allowed_bsize(cm, i))
av1_cost_tokens_from_cdf(x->filter_intra_cost[i],
fc->filter_intra_cdfs[i], NULL);
}
for (i = 0; i < SWITCHABLE_FILTER_CONTEXTS; ++i)
av1_cost_tokens_from_cdf(x->switchable_interp_costs[i],
fc->switchable_interp_cdf[i], NULL);
for (i = 0; i < PALATTE_BSIZE_CTXS; ++i) {
av1_cost_tokens_from_cdf(x->palette_y_size_cost[i],
fc->palette_y_size_cdf[i], NULL);
av1_cost_tokens_from_cdf(x->palette_uv_size_cost[i],
fc->palette_uv_size_cdf[i], NULL);
for (j = 0; j < PALETTE_Y_MODE_CONTEXTS; ++j) {
av1_cost_tokens_from_cdf(x->palette_y_mode_cost[i][j],
fc->palette_y_mode_cdf[i][j], NULL);
}
}
for (i = 0; i < PALETTE_UV_MODE_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->palette_uv_mode_cost[i],
fc->palette_uv_mode_cdf[i], NULL);
}
for (i = 0; i < PALETTE_SIZES; ++i) {
for (j = 0; j < PALETTE_COLOR_INDEX_CONTEXTS; ++j) {
av1_cost_tokens_from_cdf(x->palette_y_color_cost[i][j],
fc->palette_y_color_index_cdf[i][j], NULL);
av1_cost_tokens_from_cdf(x->palette_uv_color_cost[i][j],
fc->palette_uv_color_index_cdf[i][j], NULL);
}
}
int sign_cost[CFL_JOINT_SIGNS];
av1_cost_tokens_from_cdf(sign_cost, fc->cfl_sign_cdf, NULL);
for (int joint_sign = 0; joint_sign < CFL_JOINT_SIGNS; joint_sign++) {
int *cost_u = x->cfl_cost[joint_sign][CFL_PRED_U];
int *cost_v = x->cfl_cost[joint_sign][CFL_PRED_V];
if (CFL_SIGN_U(joint_sign) == CFL_SIGN_ZERO) {
memset(cost_u, 0, CFL_ALPHABET_SIZE * sizeof(*cost_u));
} else {
const aom_cdf_prob *cdf_u = fc->cfl_alpha_cdf[CFL_CONTEXT_U(joint_sign)];
av1_cost_tokens_from_cdf(cost_u, cdf_u, NULL);
}
if (CFL_SIGN_V(joint_sign) == CFL_SIGN_ZERO) {
memset(cost_v, 0, CFL_ALPHABET_SIZE * sizeof(*cost_v));
} else {
const aom_cdf_prob *cdf_v = fc->cfl_alpha_cdf[CFL_CONTEXT_V(joint_sign)];
av1_cost_tokens_from_cdf(cost_v, cdf_v, NULL);
}
for (int u = 0; u < CFL_ALPHABET_SIZE; u++)
cost_u[u] += sign_cost[joint_sign];
}
for (i = 0; i < MAX_TX_CATS; ++i)
for (j = 0; j < TX_SIZE_CONTEXTS; ++j)
av1_cost_tokens_from_cdf(x->tx_size_cost[i][j], fc->tx_size_cdf[i][j],
NULL);
for (i = 0; i < TXFM_PARTITION_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->txfm_partition_cost[i],
fc->txfm_partition_cdf[i], NULL);
}
for (i = TX_4X4; i < EXT_TX_SIZES; ++i) {
int s;
for (s = 1; s < EXT_TX_SETS_INTER; ++s) {
if (use_inter_ext_tx_for_txsize[s][i]) {
av1_cost_tokens_from_cdf(
x->inter_tx_type_costs[s][i], fc->inter_ext_tx_cdf[s][i],
av1_ext_tx_inv[av1_ext_tx_set_idx_to_type[1][s]]);
}
}
for (s = 1; s < EXT_TX_SETS_INTRA; ++s) {
if (use_intra_ext_tx_for_txsize[s][i]) {
for (j = 0; j < INTRA_MODES; ++j) {
av1_cost_tokens_from_cdf(
x->intra_tx_type_costs[s][i][j], fc->intra_ext_tx_cdf[s][i][j],
av1_ext_tx_inv[av1_ext_tx_set_idx_to_type[0][s]]);
}
}
}
}
for (i = 0; i < DIRECTIONAL_MODES; ++i) {
av1_cost_tokens_from_cdf(x->angle_delta_cost[i], fc->angle_delta_cdf[i],
NULL);
}
av1_cost_tokens_from_cdf(x->switchable_restore_cost,
fc->switchable_restore_cdf, NULL);
av1_cost_tokens_from_cdf(x->wiener_restore_cost, fc->wiener_restore_cdf,
NULL);
av1_cost_tokens_from_cdf(x->sgrproj_restore_cost, fc->sgrproj_restore_cdf,
NULL);
av1_cost_tokens_from_cdf(x->intrabc_cost, fc->intrabc_cdf, NULL);
if (!frame_is_intra_only(cm)) {
for (i = 0; i < COMP_INTER_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->comp_inter_cost[i], fc->comp_inter_cdf[i],
NULL);
}
for (i = 0; i < REF_CONTEXTS; ++i) {
for (j = 0; j < SINGLE_REFS - 1; ++j) {
av1_cost_tokens_from_cdf(x->single_ref_cost[i][j],
fc->single_ref_cdf[i][j], NULL);
}
}
for (i = 0; i < COMP_REF_TYPE_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->comp_ref_type_cost[i],
fc->comp_ref_type_cdf[i], NULL);
}
for (i = 0; i < UNI_COMP_REF_CONTEXTS; ++i) {
for (j = 0; j < UNIDIR_COMP_REFS - 1; ++j) {
av1_cost_tokens_from_cdf(x->uni_comp_ref_cost[i][j],
fc->uni_comp_ref_cdf[i][j], NULL);
}
}
for (i = 0; i < REF_CONTEXTS; ++i) {
for (j = 0; j < FWD_REFS - 1; ++j) {
av1_cost_tokens_from_cdf(x->comp_ref_cost[i][j], fc->comp_ref_cdf[i][j],
NULL);
}
}
for (i = 0; i < REF_CONTEXTS; ++i) {
for (j = 0; j < BWD_REFS - 1; ++j) {
av1_cost_tokens_from_cdf(x->comp_bwdref_cost[i][j],
fc->comp_bwdref_cdf[i][j], NULL);
}
}
for (i = 0; i < INTRA_INTER_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->intra_inter_cost[i], fc->intra_inter_cdf[i],
NULL);
}
for (i = 0; i < NEWMV_MODE_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->newmv_mode_cost[i], fc->newmv_cdf[i], NULL);
}
for (i = 0; i < GLOBALMV_MODE_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->zeromv_mode_cost[i], fc->zeromv_cdf[i], NULL);
}
for (i = 0; i < REFMV_MODE_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->refmv_mode_cost[i], fc->refmv_cdf[i], NULL);
}
for (i = 0; i < DRL_MODE_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->drl_mode_cost0[i], fc->drl_cdf[i], NULL);
}
for (i = 0; i < INTER_MODE_CONTEXTS; ++i)
av1_cost_tokens_from_cdf(x->inter_compound_mode_cost[i],
fc->inter_compound_mode_cdf[i], NULL);
for (i = 0; i < BLOCK_SIZES_ALL; ++i)
av1_cost_tokens_from_cdf(x->compound_type_cost[i],
fc->compound_type_cdf[i], NULL);
for (i = 0; i < BLOCK_SIZES_ALL; ++i) {
if (get_interinter_wedge_bits(i)) {
av1_cost_tokens_from_cdf(x->wedge_idx_cost[i], fc->wedge_idx_cdf[i],
NULL);
}
}
for (i = 0; i < BLOCK_SIZE_GROUPS; ++i) {
av1_cost_tokens_from_cdf(x->interintra_cost[i], fc->interintra_cdf[i],
NULL);
av1_cost_tokens_from_cdf(x->interintra_mode_cost[i],
fc->interintra_mode_cdf[i], NULL);
}
for (i = 0; i < BLOCK_SIZES_ALL; ++i) {
av1_cost_tokens_from_cdf(x->wedge_interintra_cost[i],
fc->wedge_interintra_cdf[i], NULL);
}
for (i = BLOCK_8X8; i < BLOCK_SIZES_ALL; i++) {
av1_cost_tokens_from_cdf(x->motion_mode_cost[i], fc->motion_mode_cdf[i],
NULL);
}
for (i = BLOCK_8X8; i < BLOCK_SIZES_ALL; i++) {
av1_cost_tokens_from_cdf(x->motion_mode_cost1[i], fc->obmc_cdf[i], NULL);
}
for (i = 0; i < COMP_INDEX_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->comp_idx_cost[i], fc->compound_index_cdf[i],
NULL);
}
for (i = 0; i < COMP_GROUP_IDX_CONTEXTS; ++i) {
av1_cost_tokens_from_cdf(x->comp_group_idx_cost[i],
fc->comp_group_idx_cdf[i], NULL);
}
}
}
// Values are now correlated to quantizer.
static int sad_per_bit16lut_8[QINDEX_RANGE];
static int sad_per_bit4lut_8[QINDEX_RANGE];
static int sad_per_bit16lut_10[QINDEX_RANGE];
static int sad_per_bit4lut_10[QINDEX_RANGE];
static int sad_per_bit16lut_12[QINDEX_RANGE];
static int sad_per_bit4lut_12[QINDEX_RANGE];
static void init_me_luts_bd(int *bit16lut, int *bit4lut, int range,
aom_bit_depth_t bit_depth) {
int i;
// Initialize the sad lut tables using a formulaic calculation for now.
// This is to make it easier to resolve the impact of experimental changes
// to the quantizer tables.
for (i = 0; i < range; i++) {
const double q = av1_convert_qindex_to_q(i, bit_depth);
bit16lut[i] = (int)(0.0418 * q + 2.4107);
bit4lut[i] = (int)(0.063 * q + 2.742);
}
}
void av1_init_me_luts(void) {
init_me_luts_bd(sad_per_bit16lut_8, sad_per_bit4lut_8, QINDEX_RANGE,
AOM_BITS_8);
init_me_luts_bd(sad_per_bit16lut_10, sad_per_bit4lut_10, QINDEX_RANGE,
AOM_BITS_10);
init_me_luts_bd(sad_per_bit16lut_12, sad_per_bit4lut_12, QINDEX_RANGE,
AOM_BITS_12);
}
static const int rd_boost_factor[16] = { 64, 32, 32, 32, 24, 16, 12, 12,
8, 8, 4, 4, 2, 2, 1, 0 };
static const int rd_frame_type_factor[FRAME_UPDATE_TYPES] = {
128, 144, 128, 128, 144,
// TODO(zoeliu): To adjust further following factor values.
128, 128, 128,
// TODO(weitinglin): We should investigate if the values should be the same
// as the value used by OVERLAY frame
144, // INTNL_OVERLAY_UPDATE
128 // INTNL_ARF_UPDATE
};
int av1_compute_rd_mult(const AV1_COMP *cpi, int qindex) {
const int64_t q =
av1_dc_quant_Q3(qindex, 0, cpi->common.seq_params.bit_depth);
int64_t rdmult = 0;
switch (cpi->common.seq_params.bit_depth) {
case AOM_BITS_8: rdmult = 88 * q * q / 24; break;
case AOM_BITS_10: rdmult = ROUND_POWER_OF_TWO(88 * q * q / 24, 4); break;
case AOM_BITS_12: rdmult = ROUND_POWER_OF_TWO(88 * q * q / 24, 8); break;
default:
assert(0 && "bit_depth should be AOM_BITS_8, AOM_BITS_10 or AOM_BITS_12");
return -1;
}
if (cpi->oxcf.pass == 2 && (cpi->common.frame_type != KEY_FRAME)) {
const GF_GROUP *const gf_group = &cpi->twopass.gf_group;
const FRAME_UPDATE_TYPE frame_type = gf_group->update_type[gf_group->index];
const int boost_index = AOMMIN(15, (cpi->rc.gfu_boost / 100));
rdmult = (rdmult * rd_frame_type_factor[frame_type]) >> 7;
rdmult += ((rdmult * rd_boost_factor[boost_index]) >> 7);
}
if (rdmult < 1) rdmult = 1;
return (int)rdmult;
}
static int compute_rd_thresh_factor(int qindex, aom_bit_depth_t bit_depth) {
double q;
switch (bit_depth) {
case AOM_BITS_8: q = av1_dc_quant_Q3(qindex, 0, AOM_BITS_8) / 4.0; break;
case AOM_BITS_10: q = av1_dc_quant_Q3(qindex, 0, AOM_BITS_10) / 16.0; break;
case AOM_BITS_12: q = av1_dc_quant_Q3(qindex, 0, AOM_BITS_12) / 64.0; break;
default:
assert(0 && "bit_depth should be AOM_BITS_8, AOM_BITS_10 or AOM_BITS_12");
return -1;
}
// TODO(debargha): Adjust the function below.
return AOMMAX((int)(pow(q, RD_THRESH_POW) * 5.12), 8);
}
void av1_initialize_me_consts(const AV1_COMP *cpi, MACROBLOCK *x, int qindex) {
switch (cpi->common.seq_params.bit_depth) {
case AOM_BITS_8:
x->sadperbit16 = sad_per_bit16lut_8[qindex];
x->sadperbit4 = sad_per_bit4lut_8[qindex];
break;
case AOM_BITS_10:
x->sadperbit16 = sad_per_bit16lut_10[qindex];
x->sadperbit4 = sad_per_bit4lut_10[qindex];
break;
case AOM_BITS_12:
x->sadperbit16 = sad_per_bit16lut_12[qindex];
x->sadperbit4 = sad_per_bit4lut_12[qindex];
break;
default:
assert(0 && "bit_depth should be AOM_BITS_8, AOM_BITS_10 or AOM_BITS_12");
}
}
static void set_block_thresholds(const AV1_COMMON *cm, RD_OPT *rd) {
int i, bsize, segment_id;
for (segment_id = 0; segment_id < MAX_SEGMENTS; ++segment_id) {
const int qindex =
clamp(av1_get_qindex(&cm->seg, segment_id, cm->base_qindex) +
cm->y_dc_delta_q,
0, MAXQ);
const int q = compute_rd_thresh_factor(qindex, cm->seq_params.bit_depth);
for (bsize = 0; bsize < BLOCK_SIZES_ALL; ++bsize) {
// Threshold here seems unnecessarily harsh but fine given actual
// range of values used for cpi->sf.thresh_mult[].
const int t = q * rd_thresh_block_size_factor[bsize];
const int thresh_max = INT_MAX / t;
for (i = 0; i < MAX_MODES; ++i)
rd->threshes[segment_id][bsize][i] = rd->thresh_mult[i] < thresh_max
? rd->thresh_mult[i] * t / 4
: INT_MAX;
}
}
}
void av1_set_mvcost(MACROBLOCK *x, int ref, int ref_mv_idx) {
(void)ref;
(void)ref_mv_idx;
x->mvcost = x->mv_cost_stack;
x->nmvjointcost = x->nmv_vec_cost;
}
void av1_fill_coeff_costs(MACROBLOCK *x, FRAME_CONTEXT *fc,
const int num_planes) {
const int nplanes = AOMMIN(num_planes, PLANE_TYPES);
for (int eob_multi_size = 0; eob_multi_size < 7; ++eob_multi_size) {
for (int plane = 0; plane < nplanes; ++plane) {
LV_MAP_EOB_COST *pcost = &x->eob_costs[eob_multi_size][plane];
for (int ctx = 0; ctx < 2; ++ctx) {
aom_cdf_prob *pcdf;
switch (eob_multi_size) {
case 0: pcdf = fc->eob_flag_cdf16[plane][ctx]; break;
case 1: pcdf = fc->eob_flag_cdf32[plane][ctx]; break;
case 2: pcdf = fc->eob_flag_cdf64[plane][ctx]; break;
case 3: pcdf = fc->eob_flag_cdf128[plane][ctx]; break;
case 4: pcdf = fc->eob_flag_cdf256[plane][ctx]; break;
case 5: pcdf = fc->eob_flag_cdf512[plane][ctx]; break;
case 6:
default: pcdf = fc->eob_flag_cdf1024[plane][ctx]; break;
}
av1_cost_tokens_from_cdf(pcost->eob_cost[ctx], pcdf, NULL);
}
}
}
for (int tx_size = 0; tx_size < TX_SIZES; ++tx_size) {
for (int plane = 0; plane < nplanes; ++plane) {
LV_MAP_COEFF_COST *pcost = &x->coeff_costs[tx_size][plane];
for (int ctx = 0; ctx < TXB_SKIP_CONTEXTS; ++ctx)
av1_cost_tokens_from_cdf(pcost->txb_skip_cost[ctx],
fc->txb_skip_cdf[tx_size][ctx], NULL);
for (int ctx = 0; ctx < SIG_COEF_CONTEXTS_EOB; ++ctx)
av1_cost_tokens_from_cdf(pcost->base_eob_cost[ctx],
fc->coeff_base_eob_cdf[tx_size][plane][ctx],
NULL);
for (int ctx = 0; ctx < SIG_COEF_CONTEXTS; ++ctx)
av1_cost_tokens_from_cdf(pcost->base_cost[ctx],
fc->coeff_base_cdf[tx_size][plane][ctx], NULL);
for (int ctx = 0; ctx < EOB_COEF_CONTEXTS; ++ctx)
av1_cost_tokens_from_cdf(pcost->eob_extra_cost[ctx],
fc->eob_extra_cdf[tx_size][plane][ctx], NULL);
for (int ctx = 0; ctx < DC_SIGN_CONTEXTS; ++ctx)
av1_cost_tokens_from_cdf(pcost->dc_sign_cost[ctx],
fc->dc_sign_cdf[plane][ctx], NULL);
for (int ctx = 0; ctx < LEVEL_CONTEXTS; ++ctx) {
int br_rate[BR_CDF_SIZE];
int prev_cost = 0;
int i, j;
av1_cost_tokens_from_cdf(br_rate, fc->coeff_br_cdf[tx_size][plane][ctx],
NULL);
// printf("br_rate: ");
// for(j = 0; j < BR_CDF_SIZE; j++)
// printf("%4d ", br_rate[j]);
// printf("\n");
for (i = 0; i < COEFF_BASE_RANGE; i += BR_CDF_SIZE - 1) {
for (j = 0; j < BR_CDF_SIZE - 1; j++) {
pcost->lps_cost[ctx][i + j] = prev_cost + br_rate[j];
}
prev_cost += br_rate[j];
}
pcost->lps_cost[ctx][i] = prev_cost;
// printf("lps_cost: %d %d %2d : ", tx_size, plane, ctx);
// for (i = 0; i <= COEFF_BASE_RANGE; i++)
// printf("%5d ", pcost->lps_cost[ctx][i]);
// printf("\n");
}
}
}
}
void av1_initialize_rd_consts(AV1_COMP *cpi) {
AV1_COMMON *const cm = &cpi->common;
MACROBLOCK *const x = &cpi->td.mb;
RD_OPT *const rd = &cpi->rd;
aom_clear_system_state();
rd->RDMULT = av1_compute_rd_mult(cpi, cm->base_qindex + cm->y_dc_delta_q);
set_error_per_bit(x, rd->RDMULT);
set_block_thresholds(cm, rd);
if (cm->cur_frame_force_integer_mv) {
av1_build_nmv_cost_table(x->nmv_vec_cost, x->nmvcost, &cm->fc->nmvc,
MV_SUBPEL_NONE);
} else {
av1_build_nmv_cost_table(
x->nmv_vec_cost,
cm->allow_high_precision_mv ? x->nmvcost_hp : x->nmvcost, &cm->fc->nmvc,
cm->allow_high_precision_mv);
}
x->mvcost = x->mv_cost_stack;
x->nmvjointcost = x->nmv_vec_cost;
if (frame_is_intra_only(cm) && cm->allow_screen_content_tools &&
cpi->oxcf.pass != 1) {
int *dvcost[2] = { &cpi->dv_cost[0][MV_MAX], &cpi->dv_cost[1][MV_MAX] };
av1_build_nmv_cost_table(cpi->dv_joint_cost, dvcost, &cm->fc->ndvc,
MV_SUBPEL_NONE);
}
if (cpi->oxcf.pass != 1) {
for (int i = 0; i < TRANS_TYPES; ++i)
// IDENTITY: 1 bit
// TRANSLATION: 3 bits
// ROTZOOM: 2 bits
// AFFINE: 3 bits
cpi->gmtype_cost[i] = (1 + (i > 0 ? (i == ROTZOOM ? 1 : 2) : 0))
<< AV1_PROB_COST_SHIFT;
}
}
static void model_rd_norm(int xsq_q10, int *r_q10, int *d_q10) {
// NOTE: The tables below must be of the same size.
// The functions described below are sampled at the four most significant
// bits of x^2 + 8 / 256.
// Normalized rate:
// This table models the rate for a Laplacian source with given variance
// when quantized with a uniform quantizer with given stepsize. The
// closed form expression is:
// Rn(x) = H(sqrt(r)) + sqrt(r)*[1 + H(r)/(1 - r)],
// where r = exp(-sqrt(2) * x) and x = qpstep / sqrt(variance),
// and H(x) is the binary entropy function.
static const int rate_tab_q10[] = {
65536, 6086, 5574, 5275, 5063, 4899, 4764, 4651, 4553, 4389, 4255, 4142,
4044, 3958, 3881, 3811, 3748, 3635, 3538, 3453, 3376, 3307, 3244, 3186,
3133, 3037, 2952, 2877, 2809, 2747, 2690, 2638, 2589, 2501, 2423, 2353,
2290, 2232, 2179, 2130, 2084, 2001, 1928, 1862, 1802, 1748, 1698, 1651,
1608, 1530, 1460, 1398, 1342, 1290, 1243, 1199, 1159, 1086, 1021, 963,
911, 864, 821, 781, 745, 680, 623, 574, 530, 490, 455, 424,
395, 345, 304, 269, 239, 213, 190, 171, 154, 126, 104, 87,
73, 61, 52, 44, 38, 28, 21, 16, 12, 10, 8, 6,
5, 3, 2, 1, 1, 1, 0, 0,
};
// Normalized distortion:
// This table models the normalized distortion for a Laplacian source
// with given variance when quantized with a uniform quantizer
// with given stepsize. The closed form expression is:
// Dn(x) = 1 - 1/sqrt(2) * x / sinh(x/sqrt(2))
// where x = qpstep / sqrt(variance).
// Note the actual distortion is Dn * variance.
static const int dist_tab_q10[] = {
0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5,
5, 6, 7, 7, 8, 9, 11, 12, 13, 15, 16, 17,
18, 21, 24, 26, 29, 31, 34, 36, 39, 44, 49, 54,
59, 64, 69, 73, 78, 88, 97, 106, 115, 124, 133, 142,
151, 167, 184, 200, 215, 231, 245, 260, 274, 301, 327, 351,
375, 397, 418, 439, 458, 495, 528, 559, 587, 613, 637, 659,
680, 717, 749, 777, 801, 823, 842, 859, 874, 899, 919, 936,
949, 960, 969, 977, 983, 994, 1001, 1006, 1010, 1013, 1015, 1017,
1018, 1020, 1022, 1022, 1023, 1023, 1023, 1024,
};
static const int xsq_iq_q10[] = {
0, 4, 8, 12, 16, 20, 24, 28, 32,
40, 48, 56, 64, 72, 80, 88, 96, 112,
128, 144, 160, 176, 192, 208, 224, 256, 288,
320, 352, 384, 416, 448, 480, 544, 608, 672,
736, 800, 864, 928, 992, 1120, 1248, 1376, 1504,
1632, 1760, 1888, 2016, 2272, 2528, 2784, 3040, 3296,
3552, 3808, 4064, 4576, 5088, 5600, 6112, 6624, 7136,
7648, 8160, 9184, 10208, 11232, 12256, 13280, 14304, 15328,
16352, 18400, 20448, 22496, 24544, 26592, 28640, 30688, 32736,
36832, 40928, 45024, 49120, 53216, 57312, 61408, 65504, 73696,
81888, 90080, 98272, 106464, 114656, 122848, 131040, 147424, 163808,
180192, 196576, 212960, 229344, 245728,
};
const int tmp = (xsq_q10 >> 2) + 8;
const int k = get_msb(tmp) - 3;
const int xq = (k << 3) + ((tmp >> k) & 0x7);
const int one_q10 = 1 << 10;
const int a_q10 = ((xsq_q10 - xsq_iq_q10[xq]) << 10) >> (2 + k);
const int b_q10 = one_q10 - a_q10;
*r_q10 = (rate_tab_q10[xq] * b_q10 + rate_tab_q10[xq + 1] * a_q10) >> 10;
*d_q10 = (dist_tab_q10[xq] * b_q10 + dist_tab_q10[xq + 1] * a_q10) >> 10;
}
void av1_model_rd_from_var_lapndz(int64_t var, unsigned int n_log2,
unsigned int qstep, int *rate,
int64_t *dist) {
// This function models the rate and distortion for a Laplacian
// source with given variance when quantized with a uniform quantizer
// with given stepsize. The closed form expressions are in:
// Hang and Chen, "Source Model for transform video coder and its
// application - Part I: Fundamental Theory", IEEE Trans. Circ.
// Sys. for Video Tech., April 1997.
if (var == 0) {
*rate = 0;
*dist = 0;
} else {
int d_q10, r_q10;
static const uint32_t MAX_XSQ_Q10 = 245727;
const uint64_t xsq_q10_64 =
(((uint64_t)qstep * qstep << (n_log2 + 10)) + (var >> 1)) / var;
const int xsq_q10 = (int)AOMMIN(xsq_q10_64, MAX_XSQ_Q10);
model_rd_norm(xsq_q10, &r_q10, &d_q10);
*rate = ROUND_POWER_OF_TWO(r_q10 << n_log2, 10 - AV1_PROB_COST_SHIFT);
*dist = (var * (int64_t)d_q10 + 512) >> 10;
}
}
static double interp_cubic(const double *p, double x) {
return p[1] + 0.5 * x *
(p[2] - p[0] +
x * (2.0 * p[0] - 5.0 * p[1] + 4.0 * p[2] - p[3] +
x * (3.0 * (p[1] - p[2]) + p[3] - p[0])));
}
static double interp_bicubic(const double *p, int p_stride, double x,
double y) {
double q[4];
q[0] = interp_cubic(p, x);
q[1] = interp_cubic(p + p_stride, x);
q[2] = interp_cubic(p + 2 * p_stride, x);
q[3] = interp_cubic(p + 3 * p_stride, x);
return interp_cubic(q, y);
}
static const double interp_rgrid_surf[65 * 18] = {
0.104019, 0.245714, 0.293686, 0.358635, 0.382167, 0.412446,
0.419955, 0.421388, 0.426672, 0.427990, 0.428531, 0.456868,
0.569880, 0.638822, 1.016319, 2.143453, 3.565229, 4.720880,
0.124618, 0.294211, 0.352023, 0.429991, 0.458206, 0.494510,
0.503513, 0.505232, 0.511566, 0.513234, 0.519365, 0.570225,
0.697373, 0.840624, 1.462198, 3.289054, 6.256517, 6.852788,
0.118630, 0.269669, 0.346620, 0.430999, 0.459385, 0.495783,
0.504808, 0.506532, 0.512884, 0.514988, 0.543437, 0.662772,
0.795876, 1.313596, 2.403841, 4.163098, 7.440589, 8.616275,
0.093329, 0.168205, 0.321320, 0.430607, 0.459385, 0.495783,
0.504813, 0.506548, 0.512975, 0.520662, 0.571659, 0.701841,
1.010727, 2.138851, 3.460626, 6.317955, 10.098127, 14.418553,
0.087021, 0.142905, 0.315011, 0.430509, 0.459385, 0.495787,
0.505075, 0.507599, 0.513584, 0.543182, 0.669941, 0.825620,
1.362800, 2.572187, 4.205047, 7.498399, 12.303118, 16.641735,
0.086923, 0.142513, 0.314913, 0.430508, 0.459385, 0.495803,
0.506126, 0.511816, 0.514810, 0.549705, 0.725350, 1.127334,
2.168597, 3.463686, 6.318605, 10.162284, 18.556041, 19.847042,
0.086923, 0.142513, 0.314913, 0.430506, 0.459376, 0.495805,
0.506388, 0.512954, 0.520772, 0.580215, 0.810474, 1.391548,
2.579442, 4.205160, 7.498399, 12.381597, 21.703618, 24.015457,
0.086923, 0.142513, 0.314911, 0.430353, 0.458765, 0.495652,
0.506391, 0.513406, 0.544098, 0.702950, 1.121860, 2.168961,
3.463798, 6.318607, 10.162284, 18.685361, 28.188192, 37.638872,
0.086923, 0.142513, 0.314901, 0.429742, 0.456313, 0.495045,
0.506484, 0.519195, 0.580104, 0.810126, 1.391462, 2.579441,
4.205160, 7.498399, 12.381597, 21.848607, 33.367199, 42.623190,
0.086923, 0.142513, 0.314899, 0.429589, 0.455706, 0.495155,
0.507882, 0.542426, 0.702360, 1.119921, 2.168478, 3.463791,
6.318607, 10.162284, 18.685361, 28.345760, 47.802028, 49.163533,
0.086924, 0.142548, 0.315086, 0.429842, 0.455870, 0.496336,
0.512412, 0.556953, 0.773373, 1.266396, 2.548277, 4.204676,
7.498399, 12.381597, 21.848607, 33.548250, 54.301011, 56.262859,
0.087067, 0.144957, 0.327436, 0.446616, 0.466362, 0.505706,
0.522077, 0.610747, 0.972543, 1.666916, 3.338812, 6.316669,
10.162284, 18.685361, 28.345760, 48.065311, 66.145302, 78.396020,
0.094295, 0.164235, 0.393722, 0.534219, 0.530922, 0.579308,
0.603889, 0.760870, 1.229961, 2.423214, 4.173513, 7.497916,
12.381597, 21.848607, 33.548250, 54.589585, 74.875848, 86.468182,
0.124096, 0.213005, 0.497188, 0.665176, 0.685973, 0.800200,
0.911394, 1.077971, 1.677290, 3.332129, 6.314960, 10.162257,
18.685361, 28.345760, 48.065311, 66.453506, 98.275189, 96.862588,
0.140999, 0.270140, 0.658212, 0.867661, 0.970183, 1.149516,
1.480599, 1.664833, 2.421893, 3.857981, 7.418830, 12.380371,
21.848607, 33.548250, 54.589585, 75.188867, 106.657971, 99.762997,
0.178353, 0.398001, 0.988462, 1.241473, 1.340967, 1.713568,
2.335030, 2.701432, 3.348532, 5.077158, 9.829903, 18.676528,
28.345700, 48.065311, 66.453506, 98.588283, 117.057193, 101.130722,
0.281079, 0.548300, 1.395825, 1.780770, 2.000508, 2.702964,
3.638454, 4.573843, 5.051641, 7.079129, 11.293332, 21.594861,
33.544335, 54.589585, 75.188867, 106.971065, 119.957601, 101.466632,
0.476762, 0.842189, 2.019678, 2.723895, 3.188467, 4.011610,
5.545111, 7.508984, 8.176339, 9.774504, 14.720782, 27.334416,
48.049609, 66.453506, 98.588283, 117.370357, 121.329855, 101.509242,
0.993999, 1.520111, 3.013605, 4.203530, 4.982992, 6.074944,
8.583581, 11.818375, 14.192544, 14.937517, 21.258160, 33.305953,
54.585735, 75.188867, 106.971135, 120.279824, 121.976055, 102.690130,
1.776487, 2.613655, 4.356487, 6.161726, 7.622196, 9.464193,
13.077233, 18.051656, 23.221051, 24.080068, 30.085038, 48.345269,
66.457698, 98.588353, 117.379415, 121.976128, 124.356210, 107.713202,
3.191085, 4.495201, 5.686033, 8.365566, 11.275339, 14.706437,
20.300969, 28.152237, 35.688355, 39.341382, 41.030743, 55.752262,
75.211764, 106.980285, 120.608403, 124.680746, 130.222528, 112.260098,
6.136611, 7.305215, 7.272532, 10.646713, 15.630815, 22.383168,
31.349131, 42.419822, 52.301680, 58.983454, 58.915405, 69.161305,
98.992460, 117.713855, 124.344836, 130.623638, 138.442401, 127.846670,
11.707980, 13.490761, 11.640845, 14.176132, 22.131124, 33.776462,
47.365711, 61.603834, 75.281056, 83.463985, 85.510533, 86.026513,
108.787480, 123.031136, 130.607284, 138.954406, 160.867784, 158.958882,
27.062874, 32.195139, 24.147297, 22.114632, 35.580506, 52.551674,
71.652956, 88.606776, 102.107193, 110.703186, 114.398733, 111.118539,
121.503578, 132.455924, 139.490806, 161.412674, 193.563210, 172.203945,
35.625692, 47.953028, 42.639820, 42.276254, 58.815664, 84.977282,
110.656412, 126.168446, 134.658126, 140.604482, 144.006012, 141.702382,
140.125323, 153.122630, 164.748041, 194.156197, 206.854650, 174.013079,
49.516447, 65.335381, 71.738306, 81.872819, 98.400740, 136.840488,
163.775802, 169.440078, 172.747876, 171.222919, 171.679604, 172.173550,
168.200129, 187.617133, 199.683394, 207.768200, 210.062520, 175.478356,
60.341673, 92.487135, 119.907299, 136.068010, 144.778950, 189.443534,
220.120077, 219.641635, 214.616503, 205.894657, 198.453924, 200.013069,
195.938103, 206.118661, 210.447375, 212.061379, 216.078218, 181.162805,
78.422159, 112.242899, 158.416312, 181.404320, 193.188690, 229.296967,
270.461799, 275.168977, 256.511701, 244.706786, 231.344608, 226.065087,
222.248618, 218.662324, 217.966722, 218.248574, 218.818588, 182.740573,
88.713664, 123.594164, 172.928179, 213.781414, 245.800351, 252.063414,
313.283141, 331.703831, 305.866639, 285.177142, 269.759635, 251.988739,
245.998388, 232.688076, 230.588702, 230.882657, 230.319053, 192.120741,
102.540561, 152.905927, 189.137131, 241.806756, 273.868497, 284.258017,
339.689853, 373.561104, 362.657463, 326.291984, 311.922687, 290.460189,
276.774381, 273.012072, 277.751792, 279.123748, 278.820447, 233.813798,
132.983118, 176.307242, 197.415684, 243.307787, 280.893995, 332.922370,
340.329043, 404.530166, 419.475405, 375.775209, 351.300889, 340.042759,
315.683832, 306.123530, 306.359319, 306.733063, 307.609556, 261.647847,
149.579109, 185.925581, 207.937033, 245.159084, 301.890957, 350.040480,
352.250771, 418.742329, 458.112686, 430.125208, 386.460441, 380.346839,
354.679150, 337.305620, 334.504124, 335.889932, 341.060725, 286.898578,
153.576812, 202.105624, 219.366967, 248.524506, 314.255692, 350.607526,
390.567688, 408.629209, 488.000213, 480.563823, 432.461799, 410.412624,
398.607371, 400.188740, 402.780916, 408.853470, 430.449735, 363.777088,
161.353129, 214.848904, 231.549852, 258.536466, 313.163177, 368.140577,
412.136393, 413.409032, 499.838438, 519.571063, 485.833867, 444.562715,
435.738129, 442.358549, 450.166531, 453.208524, 458.424358, 385.823139,
175.109034, 227.608058, 250.069563, 286.101747, 312.256740, 378.421485,
413.344147, 435.058646, 476.960941, 542.448886, 530.189154, 495.408402,
475.326752, 465.017144, 464.694045, 465.144689, 466.905382, 398.669138,
184.750180, 240.766694, 283.240772, 305.480150, 322.409001, 374.526162,
427.141326, 452.840323, 472.604139, 545.366105, 567.676694, 541.666203,
509.591873, 492.044219, 492.778569, 493.765684, 493.235693, 413.684325,
194.728357, 254.928927, 289.991157, 300.193195, 324.194589, 371.563147,
439.226438, 468.295088, 495.654854, 533.506353, 587.476353, 578.298989,
548.041942, 527.393885, 538.965146, 545.070442, 544.295454, 454.012211,
205.195287, 283.135677, 297.921431, 319.295927, 355.621830, 392.466463,
446.696167, 485.053519, 516.426615, 532.264584, 588.481600, 615.906737,
589.319634, 555.754316, 558.389367, 569.094521, 569.779764, 475.384946,
218.552054, 298.511016, 319.188338, 351.781666, 372.789510, 412.827434,
464.569387, 506.270203, 533.049810, 553.347364, 580.644599, 632.759854,
622.235843, 569.960552, 580.799340, 586.553714, 579.488366, 491.826482,
244.803348, 299.790203, 324.187975, 363.280782, 403.710443, 441.724083,
492.732682, 534.722691, 552.193622, 575.112647, 586.097705, 635.224970,
644.642944, 606.017786, 640.321218, 642.316989, 616.397020, 548.300111,
256.957358, 318.638991, 355.063346, 389.889307, 433.607315, 468.209001,
515.178157, 573.556591, 578.113115, 587.246475, 601.762801, 638.454644,
656.574853, 641.184609, 676.908189, 684.198162, 678.387412, 574.805864,
251.211502, 323.448532, 364.227424, 411.792704, 462.226488, 503.572288,
549.299249, 599.124071, 601.227977, 597.118176, 613.247552, 633.278532,
658.074755, 664.930719, 685.731531, 693.632845, 693.076350, 578.326477,
267.695377, 354.273736, 389.976833, 438.518178, 493.332686, 544.343027,
588.895829, 620.206193, 628.327410, 606.067827, 620.998532, 657.985256,
683.936059, 691.345257, 693.894723, 695.175306, 693.618786, 578.517148,
274.290725, 363.465288, 411.808596, 463.369805, 515.310226, 581.009306,
613.070738, 636.638714, 647.333929, 629.867603, 644.646319, 687.796202,
702.859596, 713.495479, 704.068069, 704.991807, 704.188594, 587.283658,
302.538449, 389.174737, 438.518422, 493.398902, 547.662399, 601.981814,
624.773046, 641.629484, 644.699451, 645.848784, 668.033340, 703.643523,
707.422408, 717.329600, 726.298973, 744.127507, 745.365167, 617.954068,
310.328188, 410.984766, 463.369805, 515.315010, 581.309832, 613.787792,
634.988538, 654.145284, 662.632978, 668.413496, 706.494057, 750.545471,
730.724808, 730.002100, 743.625262, 750.801609, 745.308457, 606.505800,
329.948756, 437.600191, 493.398902, 547.661910, 601.917884, 622.557745,
633.244395, 644.055898, 648.224221, 665.062911, 763.555733, 812.391078,
769.063582, 744.865168, 727.579796, 724.950408, 722.179707, 598.564510,
350.848328, 462.437458, 515.315010, 581.309823, 613.779123, 634.465309,
652.056257, 662.179143, 671.466297, 726.881256, 819.824030, 880.232789,
810.371672, 754.246481, 725.053473, 724.253390, 723.503395, 603.394909,
373.704088, 492.408266, 547.661910, 601.917884, 622.557620, 633.236320,
644.023513, 648.232514, 666.381639, 785.498283, 929.441612, 999.772800,
890.339033, 775.852504, 731.840181, 726.905100, 725.251844, 604.899901,
394.473422, 514.261306, 581.309823, 613.779123, 634.465309, 652.056257,
662.179143, 671.466557, 727.134512, 835.764144, 981.747089, 1018.462934,
939.686967, 811.276731, 739.398459, 727.365647, 725.285425, 604.923525,
419.976505, 546.538939, 601.917884, 622.557620, 633.236320, 644.023513,
648.232514, 666.381639, 785.545191, 932.841398, 1036.609617, 1026.945092,
963.822765, 840.827315, 755.532423, 730.241865, 725.366847, 604.924155,
437.281359, 580.116337, 613.779123, 634.465309, 652.056257, 662.179143,
671.466557, 727.134512, 835.764859, 981.996194, 1031.896881, 1002.544732,
881.157178, 828.151494, 799.340975, 751.314325, 728.316587, 605.005504,
464.713920, 600.649281, 622.557620, 633.236320, 644.023513, 648.232514,
666.381639, 785.545191, 932.841398, 1036.735329, 1035.037004, 995.478339,
858.093733, 823.471976, 819.881754, 798.749289, 749.440463, 607.955244,
495.880237, 612.473139, 634.465309, 652.056257, 662.179143, 671.466557,
727.134512, 835.764859, 981.996194, 1032.339788, 1031.105117, 995.303259,
857.733663, 823.435877, 822.822791, 819.873050, 796.882480, 629.038445,
510.391280, 621.158273, 633.236320, 644.023513, 648.232514, 666.381639,
785.545191, 932.841398, 1036.735329, 1035.566013, 1029.599350, 994.926093,
857.645648, 823.435143, 822.904139, 822.822791, 817.965681, 673.856962,
514.588176, 632.947715, 652.056257, 662.179143, 671.466557, 727.134512,
835.764859, 981.996194, 1032.339788, 1031.547475, 1023.835377, 972.158629,
851.968626, 823.347128, 822.904770, 822.904139, 820.752301, 684.418900,
520.013294, 631.668183, 644.023513, 648.232514, 666.381639, 785.545191,
932.841398, 1036.735329, 1035.567378, 1029.776746, 1001.044108, 880.853721,
829.201546, 822.994150, 822.904770, 822.904770, 820.792975, 684.582020,
531.253628, 650.479606, 662.179143, 671.466557, 727.134512, 835.764859,
981.996194, 1032.339788, 1031.636855, 1029.601779, 995.366703, 858.086641,
823.524524, 822.906135, 822.904770, 822.904770, 820.792975, 684.582020,
528.531744, 642.424501, 648.232514, 666.381639, 785.545191, 932.841398,
1036.735329, 1035.567378, 1030.219103, 1029.576226, 995.278687, 857.733663,
823.436508, 822.904770, 822.904770, 822.904770, 820.792975, 684.582020,
545.401164, 660.550678, 671.508859, 727.304161, 835.807162, 981.996850,
1032.339788, 1031.636855, 1030.130788, 1029.487827, 994.925709, 857.645648,
823.435143, 822.904770, 822.904770, 822.904770, 820.792975, 684.582020,
537.684760, 646.650947, 669.110131, 796.487512, 935.569890, 1036.777631,
1035.567378, 1030.219103, 1030.018584, 1023.810805, 972.158629, 851.968626,
823.347128, 822.904770, 822.904770, 822.904770, 820.792975, 684.582020,
552.408370, 670.001885, 738.246482, 879.690154, 992.939171, 1032.509436,
1031.636855, 1030.132153, 1029.665223, 1001.043724, 880.853721, 829.201546,
822.994150, 822.904770, 822.904770, 822.904770, 820.792975, 684.582020,
539.835902, 667.496388, 799.216004, 946.512211, 1039.506123, 1035.609680,
1030.219103, 1030.107964, 1029.577207, 995.366703, 858.086641, 823.524524,
822.906135, 822.904770, 822.904770, 822.904770, 820.792975, 684.582020,
558.362529, 734.277451, 877.197218, 990.478243, 1029.908393, 1028.993978,
1027.488620, 1027.464048, 1026.933674, 992.724534, 855.532488, 821.323349,
820.792975, 820.792975, 820.792975, 820.792975, 818.686600, 682.825198,
453.127195, 649.075095, 780.278390, 867.165890, 862.469711, 857.067460,
856.956321, 856.955937, 856.513579, 827.981461, 713.556496, 685.024378,
684.582020, 684.582020, 684.582020, 684.582020, 682.825198, 569.510056,
};
static const double interp_dgrid_surf[65 * 18] = {
10.650434, 12.204694, 12.040917, 11.843008, 11.845578, 12.051535, 12.103583,
12.136780, 12.266709, 12.299107, 12.299673, 12.303120, 12.316337, 12.293431,
12.092165, 11.602421, 11.141559, 8.864495, 12.770003, 14.634889, 14.437149,
14.199413, 14.202487, 14.449423, 14.511827, 14.551629, 14.707410, 14.746265,
14.747610, 14.753705, 14.762194, 14.699395, 14.390525, 13.690970, 12.874168,
10.367121, 12.832328, 14.790730, 14.503765, 14.236403, 14.239028, 14.486600,
14.549164, 14.589069, 14.745250, 14.784258, 14.788320, 14.801930, 14.762798,
14.499088, 14.021544, 13.469684, 12.661560, 10.108384, 12.950520, 15.264726,
14.621957, 14.238236, 14.239028, 14.486601, 14.549264, 14.589469, 14.745361,
14.784949, 14.791572, 14.798652, 14.660251, 14.119394, 13.651131, 12.935657,
12.176082, 9.228999, 12.979992, 15.382918, 14.651428, 14.238693, 14.239028,
14.486701, 14.555710, 14.615321, 14.751849, 14.787700, 14.797104, 14.743189,
14.475057, 13.944406, 13.450468, 12.687876, 11.824993, 8.906683, 12.980449,
15.384750, 14.651885, 14.238700, 14.239028, 14.487102, 14.581562, 14.718998,
14.777721, 14.788445, 14.778661, 14.582790, 14.099785, 13.649637, 12.935359,
12.201859, 10.891931, 8.482221, 12.980449, 15.384750, 14.651886, 14.238801,
14.239434, 14.487303, 14.588010, 14.744860, 14.784773, 14.786094, 14.735647,
14.455704, 13.939591, 13.450393, 12.687876, 11.849334, 10.476658, 8.043672,
12.980449, 15.384750, 14.651987, 14.245320, 14.265579, 14.493824, 14.588211,
14.745312, 14.787263, 14.775934, 14.582036, 14.099475, 13.649563, 12.935358,
12.201859, 10.911285, 9.730570, 6.696921, 12.980449, 15.384750, 14.652393,
14.271466, 14.370434, 14.520069, 14.589027, 14.746028, 14.785482, 14.735605,
14.455693, 13.939590, 13.450393, 12.687876, 11.849334, 10.494514, 9.195398,
6.215460, 12.980449, 15.384750, 14.652494, 14.277985, 14.396679, 14.533035,
14.615021, 14.754825, 14.775610, 14.582796, 14.099664, 13.649565, 12.935358,
12.201859, 10.911285, 9.747361, 7.779960, 5.617541, 12.980448, 15.384731,
14.652415, 14.278078, 14.397578, 14.559053, 14.718657, 14.776398, 14.747044,
14.504690, 13.951810, 13.450583, 12.687876, 11.849334, 10.494514, 9.210817,
7.210003, 5.164575, 12.980446, 15.383448, 14.647073, 14.277541, 14.403813,
14.569546, 14.744956, 14.765103, 14.629073, 14.296161, 13.698573, 12.936118,
12.201859, 10.911285, 9.747361, 7.790897, 6.322998, 3.931551, 12.981550,
15.376916, 14.615597, 14.274820, 14.437479, 14.575942, 14.707492, 14.734111,
14.515975, 14.000806, 13.462803, 12.688066, 11.849334, 10.494514, 9.210817,
7.219566, 5.781392, 3.486081, 12.991899, 15.376201, 14.579444, 14.296898,
14.473361, 14.522910, 14.491600, 14.543267, 14.288580, 13.700311, 12.936579,
12.201867, 10.911285, 9.747361, 7.790897, 6.331506, 4.480348, 2.923138,
13.019848, 15.383477, 14.582260, 14.385262, 14.452673, 14.436019, 14.238174,
14.255993, 13.977481, 13.532342, 12.705591, 11.849605, 10.494514, 9.210817,
7.219566, 5.789642, 4.018194, 2.766222, 13.028558, 15.315782, 14.439141,
14.326286, 14.452429, 14.311731, 14.033235, 13.922587, 13.665868, 13.207897,
12.274375, 10.912967, 9.747371, 7.790897, 6.331506, 4.488594, 3.454993,
2.692682, 12.992752, 15.321471, 14.409573, 14.236340, 14.322969, 14.049072,
13.764823, 13.479242, 13.250105, 12.759133, 12.019174, 10.532951, 9.211409,
7.219566, 5.789642, 4.026440, 3.298077, 2.674624, 12.945493, 15.276596,
14.315745, 14.026198, 14.085774, 13.844563, 13.447576, 12.964935, 12.735525,
12.288592, 11.511693, 9.900227, 7.793270, 6.331506, 4.488594, 3.463236,
3.224318, 2.672433, 12.757570, 15.056661, 14.095011, 13.722362, 13.812624,
13.608480, 13.021206, 12.367627, 11.937931, 11.581049, 10.599552, 9.247860,
7.220151, 5.789642, 4.026437, 3.305882, 3.191260, 2.615317, 12.581293,
14.824658, 13.909074, 13.496158, 13.491402, 13.221550, 12.514140, 11.677229,
10.936895, 10.619912, 9.634779, 7.763570, 6.331082, 4.488590, 3.462798,
3.216460, 3.076315, 2.373499, 12.283499, 14.455760, 13.890593, 13.427587,
13.183783, 12.763833, 11.861006, 10.740618, 9.820756, 9.354945, 8.669862,
7.123268, 5.787860, 4.025994, 3.290000, 3.084410, 2.810905, 2.222916,
12.010893, 14.300919, 13.986624, 13.484026, 13.025385, 12.224281, 11.064265,
9.631040, 8.594396, 8.003736, 7.561587, 6.274418, 4.466637, 3.446574,
3.102467, 2.816989, 2.598688, 1.951541, 11.581477, 13.831132, 13.632027,
13.380414, 12.807880, 11.665651, 10.218236, 8.562237, 7.222614, 6.611808,
6.261676, 5.402793, 3.938544, 3.174375, 2.818166, 2.602758, 2.213911,
1.434763, 11.050735, 12.893449, 12.363152, 12.712829, 12.012961, 10.887854,
9.109699, 7.421701, 5.965603, 5.272129, 4.991435, 4.423000, 3.369988,
2.800371, 2.593901, 2.217431, 1.670917, 1.215265, 10.641194, 11.766277,
10.777082, 10.972917, 10.689298, 9.701545, 7.719947, 6.145654, 4.872442,
4.099600, 3.880934, 3.514159, 2.786474, 2.368963, 2.162376, 1.673670,
1.450770, 1.185424, 10.071964, 11.107701, 9.172361, 8.551313, 8.412080,
7.641397, 6.174246, 4.853916, 3.904549, 3.246810, 2.959903, 2.785066,
2.240001, 1.793166, 1.585520, 1.449824, 1.405368, 1.168856, 9.213182,
9.173278, 7.219231, 6.242951, 5.626013, 5.768007, 4.908666, 3.809589,
3.115109, 2.617899, 2.274793, 2.172960, 1.838597, 1.505915, 1.414333,
1.392666, 1.338173, 1.105611, 7.365015, 7.471370, 5.622346, 4.520127,
3.936272, 4.208822, 3.623024, 2.977794, 2.450003, 2.097261, 1.824090,
1.643270, 1.473525, 1.351388, 1.327504, 1.323865, 1.307894, 1.088234,
6.198210, 6.580712, 4.682511, 3.416952, 2.941929, 2.766637, 2.650686,
2.315439, 1.925838, 1.659784, 1.464419, 1.252806, 1.162722, 1.197518,
1.199875, 1.197365, 1.194040, 0.995797, 5.402507, 5.055466, 3.728724,
2.624359, 2.165810, 1.943189, 1.918190, 1.738078, 1.516328, 1.290520,
1.155793, 1.015962, 0.881900, 0.807203, 0.754242, 0.743378, 0.740288,
0.614158, 3.937867, 3.862507, 2.884664, 2.088147, 1.648496, 1.473584,
1.340123, 1.291769, 1.165381, 1.000224, 0.893316, 0.821333, 0.691363,
0.610501, 0.586766, 0.583762, 0.577840, 0.468733, 3.104660, 3.181078,
2.420208, 1.747442, 1.297956, 1.109835, 0.970385, 0.943229, 0.876923,
0.777584, 0.678183, 0.628623, 0.553745, 0.523430, 0.519490, 0.514394,
0.492259, 0.403172, 2.593833, 2.533720, 2.010452, 1.480944, 1.060302,
0.846383, 0.738703, 0.673144, 0.658010, 0.592449, 0.518236, 0.470335,
0.425088, 0.393168, 0.378116, 0.355846, 0.275469, 0.213128, 2.176988,
2.089575, 1.671284, 1.225008, 0.895382, 0.672008, 0.566241, 0.496746,
0.488005, 0.449874, 0.400899, 0.354002, 0.318150, 0.281533, 0.238545,
0.224159, 0.202399, 0.160681, 1.874679, 1.769165, 1.430124, 1.068727,
0.780272, 0.557801, 0.441643, 0.377256, 0.352957, 0.338452, 0.304965,
0.273172, 0.240052, 0.208724, 0.193431, 0.190845, 0.185025, 0.138166,
1.590226, 1.502830, 1.193127, 0.917885, 0.670432, 0.474546, 0.355420,
0.292305, 0.259035, 0.249937, 0.232079, 0.208943, 0.181936, 0.160038,
0.152257, 0.151235, 0.149583, 0.120747, 1.331730, 1.255907, 1.012871,
0.778422, 0.578977, 0.412432, 0.293155, 0.231824, 0.197187, 0.183921,
0.174876, 0.157252, 0.140263, 0.127050, 0.110244, 0.105041, 0.104323,
0.086944, 1.153994, 1.118771, 0.822355, 0.612321, 0.478249, 0.348222,
0.247408, 0.186141, 0.152714, 0.135445, 0.129810, 0.119994, 0.115619,
0.131626, 0.095612, 0.079343, 0.077502, 0.064550, 0.946317, 0.925894,
0.677969, 0.499906, 0.397101, 0.297931, 0.214467, 0.152333, 0.120731,
0.102686, 0.095062, 0.090361, 0.122319, 0.240194, 0.112687, 0.070690,
0.070461, 0.054194, 0.824155, 0.787241, 0.581856, 0.419228, 0.313167,
0.245582, 0.183500, 0.128101, 0.096577, 0.080267, 0.071022, 0.066851,
0.085754, 0.154163, 0.075884, 0.052401, 0.054270, 0.026656, 0.716310,
0.671378, 0.489580, 0.349569, 0.256155, 0.206343, 0.157853, 0.111950,
0.079271, 0.062518, 0.053441, 0.049660, 0.051400, 0.063778, 0.039993,
0.029133, 0.023382, 0.013725, 0.614125, 0.579096, 0.417126, 0.299465,
0.217849, 0.165515, 0.129040, 0.093127, 0.065612, 0.049543, 0.041429,
0.036850, 0.034416, 0.033989, 0.024216, 0.017377, 0.014833, 0.011987,
0.520407, 0.487239, 0.349473, 0.251741, 0.184897, 0.135813, 0.107098,
0.073607, 0.053938, 0.040531, 0.032931, 0.028876, 0.025759, 0.022168,
0.016739, 0.014638, 0.014333, 0.011947, 0.449954, 0.415124, 0.299452,
0.216942, 0.158874, 0.115334, 0.088821, 0.060105, 0.042610, 0.032566,
0.026903, 0.023123, 0.019913, 0.016835, 0.014306, 0.013625, 0.013535,
0.011284, 0.377618, 0.347773, 0.251741, 0.184839, 0.132857, 0.095439,
0.070462, 0.052244, 0.036078, 0.026025, 0.021518, 0.018487, 0.015361,
0.012905, 0.011470, 0.010569, 0.010283, 0.008297, 0.319953, 0.297976,
0.216942, 0.158842, 0.113280, 0.080426, 0.057367, 0.041987, 0.030135,
0.022295, 0.017901, 0.015121, 0.012224, 0.010035, 0.009353, 0.009108,
0.008695, 0.006139, 0.267864, 0.250502, 0.184839, 0.132851, 0.095039,
0.068220, 0.049135, 0.035315, 0.025144, 0.018237, 0.013857, 0.012094,
0.009715, 0.007743, 0.006937, 0.006446, 0.006243, 0.004929, 0.230449,
0.215895, 0.158842, 0.113280, 0.080417, 0.057174, 0.041304, 0.029959,
0.021866, 0.015673, 0.012133, 0.010083, 0.007801, 0.006053, 0.005401,
0.003834, 0.003429, 0.002851, 0.193984, 0.183963, 0.132851, 0.095039,
0.068220, 0.049133, 0.035305, 0.025140, 0.018150, 0.013175, 0.010422,
0.008491, 0.006397, 0.004567, 0.003494, 0.002933, 0.002825, 0.002355,
0.167298, 0.158088, 0.113280, 0.080417, 0.057174, 0.041304, 0.029959,
0.021866, 0.015669, 0.011955, 0.009257, 0.007051, 0.005543, 0.003905,
0.002984, 0.002825, 0.002814, 0.002347, 0.143228, 0.132220, 0.095039,
0.068220, 0.049133, 0.035305, 0.025140, 0.018150, 0.013174, 0.010394,
0.008403, 0.006661, 0.005378, 0.003545, 0.002876, 0.002818, 0.002814,
0.002347, 0.122934, 0.112735, 0.080417, 0.057174, 0.041304, 0.029959,
0.021866, 0.015669, 0.011955, 0.009258, 0.007182, 0.006012, 0.003762,
0.002866, 0.002739, 0.002788, 0.002810, 0.002347, 0.101934, 0.094569,