// SPDX-License-Identifier: Apache-2.0 // ---------------------------------------------------------------------------- // Copyright 2011-2021 Arm Limited // // Licensed under the Apache License, Version 2.0 (the "License"); you may not // use this file except in compliance with the License. You may obtain a copy // of the License at: // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, WITHOUT // WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the // License for the specific language governing permissions and limitations // under the License. // ---------------------------------------------------------------------------- #if !defined(ASTCENC_DECOMPRESS_ONLY) /** * @brief Functions for angular-sum algorithm for weight alignment. * * This algorithm works as follows: * - we compute a complex number P as (cos s*i, sin s*i) for each weight, * where i is the input value and s is a scaling factor based on the spacing between the weights. * - we then add together complex numbers for all the weights. * - we then compute the length and angle of the resulting sum. * * This should produce the following results: * - perfect alignment results in a vector whose length is equal to the sum of lengths of all inputs * - even distribution results in a vector of length 0. * - all samples identical results in perfect alignment for every scaling. * * For each scaling factor within a given set, we compute an alignment factor from 0 to 1. This * should then result in some scalings standing out as having particularly good alignment factors; * we can use this to produce a set of candidate scale/shift values for various quantization levels; * we should then actually try them and see what happens. */ #include "astcenc_internal.h" #include "astcenc_vecmathlib.h" #include #include #include static constexpr unsigned int ANGULAR_STEPS { 40 }; // Store a reduced sin/cos table for 64 possible weight values; this causes slight quality loss // compared to using sin() and cos() directly. Must be 2^N. static constexpr unsigned int SINCOS_STEPS { 64 }; static_assert((ANGULAR_STEPS % ASTCENC_SIMD_WIDTH) == 0, "ANGULAR_STEPS must be multiple of ASTCENC_SIMD_WIDTH"); static unsigned int max_angular_steps_needed_for_quant_level[13]; // The next-to-last entry is supposed to have the value 33. This because the 32-weight mode leaves a // double-sized hole in the middle of the weight space, so we are better off matching 33 weights. static const unsigned int quantization_steps_for_level[13] { 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 33, 36 }; alignas(ASTCENC_VECALIGN) static float sin_table[SINCOS_STEPS][ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) static float cos_table[SINCOS_STEPS][ANGULAR_STEPS]; #if !defined(NDEBUG) static bool print_once { true }; #endif /* See header for documentation. */ void prepare_angular_tables() { unsigned int max_angular_steps_needed_for_quant_steps[ANGULAR_STEPS + 1]; for (unsigned int i = 0; i < ANGULAR_STEPS; i++) { float angle_step = (float)(i + 1); for (unsigned int j = 0; j < SINCOS_STEPS; j++) { sin_table[j][i] = static_cast(sinf((2.0f * astc::PI / (SINCOS_STEPS - 1.0f)) * angle_step * static_cast(j))); cos_table[j][i] = static_cast(cosf((2.0f * astc::PI / (SINCOS_STEPS - 1.0f)) * angle_step * static_cast(j))); } max_angular_steps_needed_for_quant_steps[i + 1] = astc::min(i + 1, ANGULAR_STEPS - 1); } for (unsigned int i = 0; i < 13; i++) { max_angular_steps_needed_for_quant_level[i] = max_angular_steps_needed_for_quant_steps[quantization_steps_for_level[i]]; } } /** * @brief Compute the angular alignment factors and offsets. * * @param weight_count The number of (decimated) weights. * @param dec_weight_quant_uvalue The decimated and quantized weight values. * @param dec_weight_quant_sig The significance of each weight. * @param max_angular_steps The maximum number of steps to be tested. * @param[out] offsets The output angular offsets array. */ static void compute_angular_offsets( unsigned int weight_count, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, unsigned int max_angular_steps, float* offsets ) { promise(weight_count > 0); promise(max_angular_steps > 0); alignas(ASTCENC_VECALIGN) int isamplev[BLOCK_MAX_WEIGHTS] { 0 }; // Precompute isample; arrays are always allocated 64 elements long for (unsigned int i = 0; i < weight_count; i += ASTCENC_SIMD_WIDTH) { // Add 2^23 and interpreting bits extracts round-to-nearest int vfloat sample = loada(dec_weight_quant_uvalue + i) * (SINCOS_STEPS - 1.0f) + vfloat(12582912.0f); vint isample = float_as_int(sample) & vint((SINCOS_STEPS - 1)); storea(isample, isamplev + i); } // Arrays are multiple of SIMD width (ANGULAR_STEPS), safe to overshoot max vfloat mult = vfloat(1.0f / (2.0f * astc::PI)); for (unsigned int i = 0; i < max_angular_steps; i += ASTCENC_SIMD_WIDTH) { vfloat anglesum_x = vfloat::zero(); vfloat anglesum_y = vfloat::zero(); for (unsigned int j = 0; j < weight_count; j++) { int isample = isamplev[j]; vfloat sample_weightv(dec_weight_quant_sig[j]); anglesum_x += loada(cos_table[isample] + i) * sample_weightv; anglesum_y += loada(sin_table[isample] + i) * sample_weightv; } vfloat angle = atan2(anglesum_y, anglesum_x); vfloat ofs = angle * mult; storea(ofs, offsets + i); } } /** * @brief For a given step size compute the lowest and highest weight. * * Compute the lowest and highest weight that results from quantizing using the given stepsize and * offset, and then compute the resulting error. The cut errors indicate the error that results from * forcing samples that should have had one weight value one step up or down. * * @param weight_count The number of (decimated) weights. * @param dec_weight_quant_uvalue The decimated and quantized weight values. * @param dec_weight_quant_sig The significance of each weight. * @param max_angular_steps The maximum number of steps to be tested. * @param max_quant_steps The maximum quantization level to be tested. * @param offsets The angular offsets array. * @param[out] lowest_weight Per angular step, the lowest weight. * @param[out] weight_span Per angular step, the span between lowest and highest weight. * @param[out] error Per angular step, the error. * @param[out] cut_low_weight_error Per angular step, the low weight cut error. * @param[out] cut_high_weight_error Per angular step, the high weight cut error. */ static void compute_lowest_and_highest_weight( unsigned int weight_count, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, unsigned int max_angular_steps, unsigned int max_quant_steps, const float* offsets, int* lowest_weight, int* weight_span, float* error, float* cut_low_weight_error, float* cut_high_weight_error ) { promise(weight_count > 0); promise(max_angular_steps > 0); vfloat rcp_stepsize = vfloat::lane_id() + vfloat(1.0f); // Arrays are ANGULAR_STEPS long, so always safe to run full vectors for (unsigned int sp = 0; sp < max_angular_steps; sp += ASTCENC_SIMD_WIDTH) { vfloat minidx(128.0f); vfloat maxidx(-128.0f); vfloat errval = vfloat::zero(); vfloat cut_low_weight_err = vfloat::zero(); vfloat cut_high_weight_err = vfloat::zero(); vfloat offset = loada(&offsets[sp]); for (unsigned int j = 0; j < weight_count; ++j) { vfloat wt = load1(&dec_weight_quant_sig[j]); vfloat sval = load1(&dec_weight_quant_uvalue[j]) * rcp_stepsize - offset; vfloat svalrte = round(sval); vfloat dif = sval - svalrte; vfloat dwt = dif * wt; errval += dwt * dif; // Reset tracker on min hit vmask mask = svalrte < minidx; minidx = select(minidx, svalrte, mask); cut_low_weight_err = select(cut_low_weight_err, vfloat::zero(), mask); // Accumulate on min hit mask = svalrte == minidx; vfloat accum = cut_low_weight_err + wt - vfloat(2.0f) * dwt; cut_low_weight_err = select(cut_low_weight_err, accum, mask); // Reset tracker on max hit mask = svalrte > maxidx; maxidx = select(maxidx, svalrte, mask); cut_high_weight_err = select(cut_high_weight_err, vfloat::zero(), mask); // Accumulate on max hit mask = svalrte == maxidx; accum = cut_high_weight_err + wt + vfloat(2.0f) * dwt; cut_high_weight_err = select(cut_high_weight_err, accum, mask); } // Write out min weight and weight span; clamp span to a usable range vint span = float_to_int(maxidx - minidx + vfloat(1)); span = min(span, vint(max_quant_steps + 3)); span = max(span, vint(2)); storea(float_to_int(minidx), &lowest_weight[sp]); storea(span, &weight_span[sp]); // The cut_(lowest/highest)_weight_error indicate the error that results from forcing // samples that should have had the weight value one step (up/down). vfloat ssize = 1.0f / rcp_stepsize; vfloat errscale = ssize * ssize; storea(errval * errscale, &error[sp]); storea(cut_low_weight_err * errscale, &cut_low_weight_error[sp]); storea(cut_high_weight_err * errscale, &cut_high_weight_error[sp]); rcp_stepsize = rcp_stepsize + vfloat(ASTCENC_SIMD_WIDTH); } } /** * @brief The main function for the angular algorithm. * * @param weight_count The number of (decimated) weights. * @param dec_weight_quant_uvalue The decimated and quantized weight value. * @param dec_weight_quant_sig The significance of each weight. * @param max_quant_level The maximum quantization level to be tested. * @param[out] low_value Per angular step, the lowest weight value. * @param[out] high_value Per angular step, the highest weight value. */ static void compute_angular_endpoints_for_quant_levels( unsigned int weight_count, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, unsigned int max_quant_level, float low_value[12], float high_value[12] ) { unsigned int max_quant_steps = quantization_steps_for_level[max_quant_level]; alignas(ASTCENC_VECALIGN) float angular_offsets[ANGULAR_STEPS]; unsigned int max_angular_steps = max_angular_steps_needed_for_quant_level[max_quant_level]; compute_angular_offsets(weight_count, dec_weight_quant_uvalue, dec_weight_quant_sig, max_angular_steps, angular_offsets); alignas(ASTCENC_VECALIGN) int32_t lowest_weight[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) int32_t weight_span[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) float error[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) float cut_low_weight_error[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) float cut_high_weight_error[ANGULAR_STEPS]; compute_lowest_and_highest_weight(weight_count, dec_weight_quant_uvalue, dec_weight_quant_sig, max_angular_steps, max_quant_steps, angular_offsets, lowest_weight, weight_span, error, cut_low_weight_error, cut_high_weight_error); // For each quantization level, find the best error terms. Use packed vectors so data-dependent // branches can become selects. This involves some integer to float casts, but the values are // small enough so they never round the wrong way. vfloat4 best_results[40]; // Initialize the array to some safe defaults promise(max_quant_steps > 0); for (unsigned int i = 0; i < (max_quant_steps + 4); i++) { // Lane<0> = Best error // Lane<1> = Best scale; -1 indicates no solution found // Lane<2> = Cut low weight best_results[i] = vfloat4(ERROR_CALC_DEFAULT, -1.0f, 0.0f, 0.0f); } promise(max_angular_steps > 0); for (unsigned int i = 0; i < max_angular_steps; i++) { int idx_span = weight_span[i]; float error_cut_low = error[i] + cut_low_weight_error[i]; float error_cut_high = error[i] + cut_high_weight_error[i]; float error_cut_low_high = error[i] + cut_low_weight_error[i] + cut_high_weight_error[i]; // Check best error against record N vfloat4 best_result = best_results[idx_span]; vfloat4 new_result = vfloat4(error[i], (float)i, 0.0f, 0.0f); vmask4 mask1(best_result.lane<0>() > error[i]); best_results[idx_span] = select(best_result, new_result, mask1); // Check best error against record N-1 with either cut low or cut high best_result = best_results[idx_span - 1]; new_result = vfloat4(error_cut_low, (float)i, 1.0f, 0.0f); vmask4 mask2(best_result.lane<0>() > error_cut_low); best_result = select(best_result, new_result, mask2); new_result = vfloat4(error_cut_high, (float)i, 0.0f, 0.0f); vmask4 mask3(best_result.lane<0>() > error_cut_high); best_results[idx_span - 1] = select(best_result, new_result, mask3); // Check best error against record N-2 with both cut low and high best_result = best_results[idx_span - 2]; new_result = vfloat4(error_cut_low_high, (float)i, 1.0f, 0.0f); vmask4 mask4(best_result.lane<0>() > error_cut_low_high); best_results[idx_span - 2] = select(best_result, new_result, mask4); } for (unsigned int i = 0; i <= max_quant_level; i++) { unsigned int q = quantization_steps_for_level[i]; int bsi = (int)best_results[q].lane<1>(); // Did we find anything? #if !defined(NDEBUG) if ((bsi < 0) && print_once) { print_once = false; printf("INFO: Unable to find full encoding within search error limit.\n\n"); } #endif bsi = astc::max(0, bsi); float stepsize = 1.0f / (1.0f + (float)bsi); int lwi = lowest_weight[bsi] + (int)best_results[q].lane<2>(); int hwi = lwi + q - 1; float offset = angular_offsets[bsi] * stepsize; low_value[i] = offset + static_cast(lwi) * stepsize; high_value[i] = offset + static_cast(hwi) * stepsize; } } /** * @brief For a given step size compute the lowest and highest weight, variant for low weight count. * * Compute the lowest and highest weight that results from quantizing using the given stepsize and * offset, and then compute the resulting error. The cut errors indicate the error that results from * forcing samples that should have had one weight value one step up or down. * * @param weight_count The number of (decimated) weights. * @param dec_weight_quant_uvalue The decimated and quantized weight values. * @param dec_weight_quant_sig The significance of each weight. * @param max_angular_steps The maximum number of steps to be tested. * @param max_quant_steps The maximum quantization level to be tested. * @param offsets The angular offsets array. * @param[out] lowest_weight Per angular step, the lowest weight. * @param[out] weight_span Per angular step, the span between lowest and highest weight. * @param[out] error Per angular step, the error. */ static void compute_lowest_and_highest_weight_lwc( unsigned int weight_count, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, unsigned int max_angular_steps, unsigned int max_quant_steps, const float* offsets, int* lowest_weight, int* weight_span, float* error ) { promise(weight_count > 0); promise(max_angular_steps > 0); vfloat rcp_stepsize = vfloat::lane_id() + vfloat(1.0f); // Arrays are ANGULAR_STEPS long, so always safe to run full vectors for (unsigned int sp = 0; sp < max_angular_steps; sp += ASTCENC_SIMD_WIDTH) { vfloat minidx(128.0f); vfloat maxidx(-128.0f); vfloat errval = vfloat::zero(); vfloat offset = loada(&offsets[sp]); for (unsigned int j = 0; j < weight_count; ++j) { vfloat wt = load1(&dec_weight_quant_sig[j]); vfloat sval = load1(&dec_weight_quant_uvalue[j]) * rcp_stepsize - offset; vfloat svalrte = round(sval); vfloat dif = sval - svalrte; vfloat dwt = dif * wt; errval += dwt * dif; // Reset tracker on min hit vmask mask = svalrte < minidx; minidx = select(minidx, svalrte, mask); // Reset tracker on max hit mask = svalrte > maxidx; maxidx = select(maxidx, svalrte, mask); } // Write out min weight and weight span; clamp span to a usable range vint span = float_to_int(maxidx - minidx + vfloat(1.0f)); span = min(span, vint(max_quant_steps + 3)); span = max(span, vint(2)); storea(float_to_int(minidx), &lowest_weight[sp]); storea(span, &weight_span[sp]); // The cut_(lowest/highest)_weight_error indicate the error that results from forcing // samples that should have had the weight value one step (up/down). vfloat ssize = 1.0f / rcp_stepsize; vfloat errscale = ssize * ssize; storea(errval * errscale, &error[sp]); rcp_stepsize = rcp_stepsize + vfloat(ASTCENC_SIMD_WIDTH); } } /** * @brief The main function for the angular algorithm, variant for low weight count. * * @param weight_count The number of (decimated) weights. * @param dec_weight_quant_uvalue The decimated and quantized weight value. * @param dec_weight_quant_sig The significance of each weight. * @param max_quant_level The maximum quantization level to be tested. * @param[out] low_value Per angular step, the lowest weight value. * @param[out] high_value Per angular step, the highest weight value. */ static void compute_angular_endpoints_for_quant_levels_lwc( unsigned int weight_count, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, unsigned int max_quant_level, float low_value[12], float high_value[12] ) { unsigned int max_quant_steps = quantization_steps_for_level[max_quant_level]; unsigned int max_angular_steps = max_angular_steps_needed_for_quant_level[max_quant_level]; alignas(ASTCENC_VECALIGN) float angular_offsets[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) int32_t lowest_weight[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) int32_t weight_span[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) float error[ANGULAR_STEPS]; compute_angular_offsets(weight_count, dec_weight_quant_uvalue, dec_weight_quant_sig, max_angular_steps, angular_offsets); compute_lowest_and_highest_weight_lwc(weight_count, dec_weight_quant_uvalue, dec_weight_quant_sig, max_angular_steps, max_quant_steps, angular_offsets, lowest_weight, weight_span, error); // For each quantization level, find the best error terms. Use packed vectors so data-dependent // branches can become selects. This involves some integer to float casts, but the values are // small enough so they never round the wrong way. float best_error[ANGULAR_STEPS]; int best_index[ANGULAR_STEPS]; // Initialize the array to some safe defaults promise(max_quant_steps > 0); for (unsigned int i = 0; i < (max_quant_steps + 4); i++) { best_error[i] = ERROR_CALC_DEFAULT; best_index[i] = -1; } promise(max_angular_steps > 0); for (unsigned int i = 0; i < max_angular_steps; i++) { int idx_span = weight_span[i]; // Check best error against record N float current_best = best_error[idx_span]; if (error[i] < current_best) { best_error[idx_span] = error[i]; best_index[idx_span] = i; } } for (unsigned int i = 0; i <= max_quant_level; i++) { unsigned int q = quantization_steps_for_level[i]; int bsi = best_index[q]; // Did we find anything? #if !defined(NDEBUG) if ((bsi < 0) && print_once) { print_once = false; printf("INFO: Unable to find low weight encoding within search error limit.\n\n"); } #endif bsi = astc::max(0, bsi); int lwi = lowest_weight[bsi]; int hwi = lwi + q - 1; low_value[i] = (angular_offsets[bsi] + static_cast(lwi)) / (1.0f + (float)bsi); high_value[i] = (angular_offsets[bsi] + static_cast(hwi)) / (1.0f + (float)bsi); } } /* See header for documentation. */ void compute_angular_endpoints_1plane( unsigned int tune_low_weight_limit, bool only_always, const block_size_descriptor& bsd, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, float low_value[WEIGHTS_MAX_BLOCK_MODES], float high_value[WEIGHTS_MAX_BLOCK_MODES] ) { float low_values[WEIGHTS_MAX_DECIMATION_MODES][12]; float high_values[WEIGHTS_MAX_DECIMATION_MODES][12]; unsigned int max_decimation_modes = only_always ? bsd.always_decimation_mode_count : bsd.decimation_mode_count; promise(max_decimation_modes > 0); for (unsigned int i = 0; i < max_decimation_modes; i++) { const decimation_mode& dm = bsd.decimation_modes[i]; if (dm.maxprec_1plane < 0 || !dm.percentile_hit) { continue; } unsigned int weight_count = bsd.decimation_tables[i]->weight_count; if (weight_count < tune_low_weight_limit) { compute_angular_endpoints_for_quant_levels_lwc( weight_count, dec_weight_quant_uvalue + i * BLOCK_MAX_WEIGHTS, dec_weight_quant_sig + i * BLOCK_MAX_WEIGHTS, dm.maxprec_1plane, low_values[i], high_values[i]); } else { compute_angular_endpoints_for_quant_levels( weight_count, dec_weight_quant_uvalue + i * BLOCK_MAX_WEIGHTS, dec_weight_quant_sig + i * BLOCK_MAX_WEIGHTS, dm.maxprec_1plane, low_values[i], high_values[i]); } } unsigned int max_block_modes = only_always ? bsd.always_block_mode_count : bsd.block_mode_count; promise(max_block_modes > 0); for (unsigned int i = 0; i < max_block_modes; ++i) { const block_mode& bm = bsd.block_modes[i]; if (bm.is_dual_plane || !bm.percentile_hit) { continue; } unsigned int quant_mode = bm.quant_mode; unsigned int decim_mode = bm.decimation_mode; low_value[i] = low_values[decim_mode][quant_mode]; high_value[i] = high_values[decim_mode][quant_mode]; } } /* See header for documentation. */ void compute_angular_endpoints_2planes( unsigned int tune_low_weight_limit, const block_size_descriptor& bsd, const float* dec_weight_quant_uvalue, const float* dec_weight_quant_sig, float low_value1[WEIGHTS_MAX_BLOCK_MODES], float high_value1[WEIGHTS_MAX_BLOCK_MODES], float low_value2[WEIGHTS_MAX_BLOCK_MODES], float high_value2[WEIGHTS_MAX_BLOCK_MODES] ) { float low_values1[WEIGHTS_MAX_DECIMATION_MODES][12]; float high_values1[WEIGHTS_MAX_DECIMATION_MODES][12]; float low_values2[WEIGHTS_MAX_DECIMATION_MODES][12]; float high_values2[WEIGHTS_MAX_DECIMATION_MODES][12]; promise(bsd.decimation_mode_count > 0); for (unsigned int i = 0; i < bsd.decimation_mode_count; i++) { const decimation_mode& dm = bsd.decimation_modes[i]; if (dm.maxprec_2planes < 0 || !dm.percentile_hit) { continue; } unsigned int weight_count = bsd.decimation_tables[i]->weight_count; if (weight_count < tune_low_weight_limit) { compute_angular_endpoints_for_quant_levels_lwc( weight_count, dec_weight_quant_uvalue + i * BLOCK_MAX_WEIGHTS, dec_weight_quant_sig + i * BLOCK_MAX_WEIGHTS, dm.maxprec_2planes, low_values1[i], high_values1[i]); compute_angular_endpoints_for_quant_levels_lwc( weight_count, dec_weight_quant_uvalue + i * BLOCK_MAX_WEIGHTS + WEIGHTS_PLANE2_OFFSET, dec_weight_quant_sig + i * BLOCK_MAX_WEIGHTS + WEIGHTS_PLANE2_OFFSET, dm.maxprec_2planes, low_values2[i], high_values2[i]); } else { compute_angular_endpoints_for_quant_levels( weight_count, dec_weight_quant_uvalue + i * BLOCK_MAX_WEIGHTS, dec_weight_quant_sig + i * BLOCK_MAX_WEIGHTS, dm.maxprec_2planes, low_values1[i], high_values1[i]); compute_angular_endpoints_for_quant_levels( weight_count, dec_weight_quant_uvalue + i * BLOCK_MAX_WEIGHTS + WEIGHTS_PLANE2_OFFSET, dec_weight_quant_sig + i * BLOCK_MAX_WEIGHTS + WEIGHTS_PLANE2_OFFSET, dm.maxprec_2planes, low_values2[i], high_values2[i]); } } promise(bsd.block_mode_count > 0); for (unsigned int i = 0; i < bsd.block_mode_count; ++i) { const block_mode& bm = bsd.block_modes[i]; if (!bm.is_dual_plane || !bm.percentile_hit) { continue; } unsigned int quant_mode = bm.quant_mode; unsigned int decim_mode = bm.decimation_mode; low_value1[i] = low_values1[decim_mode][quant_mode]; high_value1[i] = high_values1[decim_mode][quant_mode]; low_value2[i] = low_values2[decim_mode][quant_mode]; high_value2[i] = high_values2[decim_mode][quant_mode]; } } #endif