// SPDX-License-Identifier: Apache-2.0 // ---------------------------------------------------------------------------- // Copyright 2011-2022 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 { 32 }; static_assert((ANGULAR_STEPS % ASTCENC_SIMD_WIDTH) == 0, "ANGULAR_STEPS must be multiple of ASTCENC_SIMD_WIDTH"); static_assert(ANGULAR_STEPS >= 32, "ANGULAR_STEPS must be at least max(steps_for_quant_level)"); // 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 const uint8_t steps_for_quant_level[12] { 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32 }; alignas(ASTCENC_VECALIGN) static float sin_table[SINCOS_STEPS][ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) static float cos_table[SINCOS_STEPS][ANGULAR_STEPS]; #if defined(ASTCENC_DIAGNOSTICS) static bool print_once { true }; #endif /* See header for documentation. */ void prepare_angular_tables() { for (unsigned int i = 0; i < ANGULAR_STEPS; i++) { float angle_step = static_cast(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))); } } } /** * @brief Compute the angular alignment factors and offsets. * * @param weight_count The number of (decimated) weights. * @param dec_weight_ideal_value The ideal decimated unquantized weight values. * @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_ideal_value, unsigned int max_angular_steps, float* offsets ) { promise(weight_count > 0); promise(max_angular_steps > 0); alignas(ASTCENC_VECALIGN) int isamplev[BLOCK_MAX_WEIGHTS]; // 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_ideal_value + 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]; anglesum_x += loada(cos_table[isample] + i); anglesum_y += loada(sin_table[isample] + i); } 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_ideal_value The ideal decimated unquantized weight values. * @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_ideal_value, unsigned int max_angular_steps, unsigned int max_quant_steps, const float* offsets, float* 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 sval = load1(dec_weight_ideal_value + j) * rcp_stepsize - offset; vfloat svalrte = round(sval); vfloat diff = sval - svalrte; errval += diff * diff; // 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 + vfloat(1.0f) - vfloat(2.0f) * diff; 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 + vfloat(1.0f) + vfloat(2.0f) * diff; 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(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_ideal_value The ideal decimated unquantized weight values. * @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_ideal_value, unsigned int max_quant_level, float low_value[TUNE_MAX_ANGULAR_QUANT + 1], float high_value[TUNE_MAX_ANGULAR_QUANT + 1] ) { unsigned int max_quant_steps = steps_for_quant_level[max_quant_level]; unsigned int max_angular_steps = steps_for_quant_level[max_quant_level]; alignas(ASTCENC_VECALIGN) float angular_offsets[ANGULAR_STEPS]; compute_angular_offsets(weight_count, dec_weight_ideal_value, max_angular_steps, angular_offsets); alignas(ASTCENC_VECALIGN) float 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_ideal_value, 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[36]; // 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++) { float i_flt = static_cast(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], i_flt, 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, i_flt, 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, i_flt, 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, i_flt, 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 = steps_for_quant_level[i]; int bsi = static_cast(best_results[q].lane<1>()); // Did we find anything? #if defined(ASTCENC_DIAGNOSTICS) 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 lwi = lowest_weight[bsi] + best_results[q].lane<2>(); float hwi = lwi + static_cast(q) - 1.0f; float stepsize = 1.0f / (1.0f + static_cast(bsi)); low_value[i] = (angular_offsets[bsi] + lwi) * stepsize; high_value[i] = (angular_offsets[bsi] + 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 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, unsigned int max_angular_steps, unsigned int max_quant_steps, const float* offsets, float* 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 sval = load1(dec_weight_quant_uvalue + j) * rcp_stepsize - offset; vfloat svalrte = round(sval); vfloat diff = sval - svalrte; errval += diff * diff; // Compute min and max quantized weight spans for each step minidx = min(minidx, svalrte); maxidx = max(maxidx, svalrte); } // 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(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_ideal_value The ideal decimated unquantized weight values. * @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_ideal_value, unsigned int max_quant_level, float low_value[TUNE_MAX_ANGULAR_QUANT + 1], float high_value[TUNE_MAX_ANGULAR_QUANT + 1] ) { unsigned int max_quant_steps = steps_for_quant_level[max_quant_level]; unsigned int max_angular_steps = steps_for_quant_level[max_quant_level]; alignas(ASTCENC_VECALIGN) float angular_offsets[ANGULAR_STEPS]; alignas(ASTCENC_VECALIGN) float 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_ideal_value, max_angular_steps, angular_offsets); compute_lowest_and_highest_weight_lwc(weight_count, dec_weight_ideal_value, 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. vfloat4 best_results[36]; // Initialize the array to some safe defaults promise(max_quant_steps > 0); for (unsigned int i = 0; i < (max_quant_steps + 4); i++) { 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]; // Check best error against record N vfloat4 current_best = best_results[idx_span]; vfloat4 candidate = vfloat4(error[i], static_cast(i), 0.0f, 0.0f); vmask4 mask(current_best.lane<0>() > error[i]); best_results[idx_span] = select(current_best, candidate, mask); } for (unsigned int i = 0; i <= max_quant_level; i++) { unsigned int q = steps_for_quant_level[i]; int bsi = static_cast(best_results[q].lane<1>()); // Did we find anything? #if defined(ASTCENC_DIAGNOSTICS) 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); float lwi = lowest_weight[bsi]; float hwi = lwi + static_cast(q) - 1.0f; float stepsize = 1.0f / (1.0f + static_cast(bsi)); low_value[i] = (angular_offsets[bsi] + lwi) * stepsize; high_value[i] = (angular_offsets[bsi] + hwi) * stepsize; } } /* 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_ideal_value, unsigned int max_weight_quant, compression_working_buffers& tmpbuf ) { float (&low_value)[WEIGHTS_MAX_BLOCK_MODES] = tmpbuf.weight_low_value1; float (&high_value)[WEIGHTS_MAX_BLOCK_MODES] = tmpbuf.weight_high_value1; float (&low_values)[WEIGHTS_MAX_DECIMATION_MODES][TUNE_MAX_ANGULAR_QUANT + 1] = tmpbuf.weight_low_values1; float (&high_values)[WEIGHTS_MAX_DECIMATION_MODES][TUNE_MAX_ANGULAR_QUANT + 1] = tmpbuf.weight_high_values1; unsigned int max_decimation_modes = only_always ? bsd.decimation_mode_count_always : bsd.decimation_mode_count_selected; 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.is_ref_1_plane(static_cast(max_weight_quant))) { continue; } unsigned int weight_count = bsd.get_decimation_info(i).weight_count; unsigned int max_precision = dm.maxprec_1plane; if (max_precision > TUNE_MAX_ANGULAR_QUANT) { max_precision = TUNE_MAX_ANGULAR_QUANT; } if (max_precision > max_weight_quant) { max_precision = max_weight_quant; } if (weight_count < tune_low_weight_limit) { compute_angular_endpoints_for_quant_levels_lwc( weight_count, dec_weight_ideal_value + i * BLOCK_MAX_WEIGHTS, max_precision, low_values[i], high_values[i]); } else { compute_angular_endpoints_for_quant_levels( weight_count, dec_weight_ideal_value + i * BLOCK_MAX_WEIGHTS, max_precision, low_values[i], high_values[i]); } } unsigned int max_block_modes = only_always ? bsd.block_mode_count_1plane_always : bsd.block_mode_count_1plane_selected; promise(max_block_modes > 0); for (unsigned int i = 0; i < max_block_modes; ++i) { const block_mode& bm = bsd.block_modes[i]; assert(!bm.is_dual_plane); unsigned int quant_mode = bm.quant_mode; unsigned int decim_mode = bm.decimation_mode; if (quant_mode <= TUNE_MAX_ANGULAR_QUANT) { low_value[i] = low_values[decim_mode][quant_mode]; high_value[i] = high_values[decim_mode][quant_mode]; } else { low_value[i] = 0.0f; high_value[i] = 1.0f; } } } /* See header for documentation. */ void compute_angular_endpoints_2planes( unsigned int tune_low_weight_limit, const block_size_descriptor& bsd, const float* dec_weight_ideal_value, unsigned int max_weight_quant, compression_working_buffers& tmpbuf ) { float (&low_value1)[WEIGHTS_MAX_BLOCK_MODES] = tmpbuf.weight_low_value1; float (&high_value1)[WEIGHTS_MAX_BLOCK_MODES] = tmpbuf.weight_high_value1; float (&low_value2)[WEIGHTS_MAX_BLOCK_MODES] = tmpbuf.weight_low_value2; float (&high_value2)[WEIGHTS_MAX_BLOCK_MODES] = tmpbuf.weight_high_value2; float (&low_values1)[WEIGHTS_MAX_DECIMATION_MODES][TUNE_MAX_ANGULAR_QUANT + 1] = tmpbuf.weight_low_values1; float (&high_values1)[WEIGHTS_MAX_DECIMATION_MODES][TUNE_MAX_ANGULAR_QUANT + 1] = tmpbuf.weight_high_values1; float (&low_values2)[WEIGHTS_MAX_DECIMATION_MODES][TUNE_MAX_ANGULAR_QUANT + 1] = tmpbuf.weight_low_values2; float (&high_values2)[WEIGHTS_MAX_DECIMATION_MODES][TUNE_MAX_ANGULAR_QUANT + 1] = tmpbuf.weight_high_values2; promise(bsd.decimation_mode_count_selected > 0); for (unsigned int i = 0; i < bsd.decimation_mode_count_selected; i++) { const decimation_mode& dm = bsd.decimation_modes[i]; if (!dm.is_ref_2_plane(static_cast(max_weight_quant))) { continue; } unsigned int weight_count = bsd.get_decimation_info(i).weight_count; unsigned int max_precision = dm.maxprec_2planes; if (max_precision > TUNE_MAX_ANGULAR_QUANT) { max_precision = TUNE_MAX_ANGULAR_QUANT; } if (max_precision > max_weight_quant) { max_precision = max_weight_quant; } if (weight_count < tune_low_weight_limit) { compute_angular_endpoints_for_quant_levels_lwc( weight_count, dec_weight_ideal_value + i * BLOCK_MAX_WEIGHTS, max_precision, low_values1[i], high_values1[i]); compute_angular_endpoints_for_quant_levels_lwc( weight_count, dec_weight_ideal_value + i * BLOCK_MAX_WEIGHTS + WEIGHTS_PLANE2_OFFSET, max_precision, low_values2[i], high_values2[i]); } else { compute_angular_endpoints_for_quant_levels( weight_count, dec_weight_ideal_value + i * BLOCK_MAX_WEIGHTS, max_precision, low_values1[i], high_values1[i]); compute_angular_endpoints_for_quant_levels( weight_count, dec_weight_ideal_value + i * BLOCK_MAX_WEIGHTS + WEIGHTS_PLANE2_OFFSET, max_precision, low_values2[i], high_values2[i]); } } unsigned int start = bsd.block_mode_count_1plane_selected; unsigned int end = bsd.block_mode_count_1plane_2plane_selected; for (unsigned int i = start; i < end; i++) { const block_mode& bm = bsd.block_modes[i]; unsigned int quant_mode = bm.quant_mode; unsigned int decim_mode = bm.decimation_mode; if (quant_mode <= TUNE_MAX_ANGULAR_QUANT) { 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]; } else { low_value1[i] = 0.0f; high_value1[i] = 1.0f; low_value2[i] = 0.0f; high_value2[i] = 1.0f; } } } #endif