mirror of https://github.com/axmolengine/axmol.git
467 lines
17 KiB
C++
467 lines
17 KiB
C++
// SPDX-License-Identifier: Apache-2.0
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// ----------------------------------------------------------------------------
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// Copyright 2011-2021 Arm Limited
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//
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// Licensed under the Apache License, Version 2.0 (the "License"); you may not
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// use this file except in compliance with the License. You may obtain a copy
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// of the License at:
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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// WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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// License for the specific language governing permissions and limitations
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// under the License.
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// ----------------------------------------------------------------------------
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#if !defined(ASTCENC_DECOMPRESS_ONLY)
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/**
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* @brief Functions for angular-sum algorithm for weight alignment.
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*
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* This algorithm works as follows:
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* - we compute a complex number P as (cos s*i, sin s*i) for each weight,
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* where i is the input value and s is a scaling factor based on the spacing between the weights.
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* - we then add together complex numbers for all the weights.
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* - we then compute the length and angle of the resulting sum.
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*
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* This should produce the following results:
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* - perfect alignment results in a vector whose length is equal to the sum of lengths of all inputs
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* - even distribution results in a vector of length 0.
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* - all samples identical results in perfect alignment for every scaling.
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*
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* For each scaling factor within a given set, we compute an alignment factor from 0 to 1. This
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* should then result in some scalings standing out as having particularly good alignment factors;
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* we can use this to produce a set of candidate scale/shift values for various quantization levels;
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* we should then actually try them and see what happens.
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*/
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#include "astcenc_internal.h"
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#include "astcenc_vecmathlib.h"
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#include <stdio.h>
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#include <cassert>
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#include <cstring>
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static constexpr unsigned int ANGULAR_STEPS { 40 };
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// Store a reduced sin/cos table for 64 possible weight values; this causes slight quality loss
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// compared to using sin() and cos() directly. Must be 2^N.
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static constexpr unsigned int SINCOS_STEPS { 64 };
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static_assert((ANGULAR_STEPS % ASTCENC_SIMD_WIDTH) == 0,
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"ANGULAR_STEPS must be multiple of ASTCENC_SIMD_WIDTH");
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static unsigned int max_angular_steps_needed_for_quant_level[13];
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// The next-to-last entry is supposed to have the value 33. This because the 32-weight mode leaves a
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// double-sized hole in the middle of the weight space, so we are better off matching 33 weights.
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static const unsigned int quantization_steps_for_level[13] = {
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2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 33, 36
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};
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alignas(ASTCENC_VECALIGN) static float sin_table[SINCOS_STEPS][ANGULAR_STEPS];
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alignas(ASTCENC_VECALIGN) static float cos_table[SINCOS_STEPS][ANGULAR_STEPS];
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/* See header for documentation. */
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void prepare_angular_tables()
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{
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unsigned int max_angular_steps_needed_for_quant_steps[ANGULAR_STEPS + 1];
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for (unsigned int i = 0; i < ANGULAR_STEPS; i++)
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{
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float angle_step = (float)(i + 1);
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for (unsigned int j = 0; j < SINCOS_STEPS; j++)
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{
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sin_table[j][i] = static_cast<float>(sinf((2.0f * astc::PI / (SINCOS_STEPS - 1.0f)) * angle_step * static_cast<float>(j)));
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cos_table[j][i] = static_cast<float>(cosf((2.0f * astc::PI / (SINCOS_STEPS - 1.0f)) * angle_step * static_cast<float>(j)));
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}
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max_angular_steps_needed_for_quant_steps[i + 1] = astc::min(i + 1, ANGULAR_STEPS - 1);
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}
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for (unsigned int i = 0; i < 13; i++)
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{
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max_angular_steps_needed_for_quant_level[i] = max_angular_steps_needed_for_quant_steps[quantization_steps_for_level[i]];
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}
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}
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/**
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* @brief Compute the angular alignment factors and offsets.
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*
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* @param sample_count The number of samples.
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* @param samples The sample data.
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* @param sample_weights The weight of each sample.
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* @param max_angular_steps The maximum number of steps to be tested.
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* @param[out] offsets The output angular offsets array.
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*/
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static void compute_angular_offsets(
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unsigned int sample_count,
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const float* samples,
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const float* sample_weights,
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unsigned int max_angular_steps,
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float* offsets
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) {
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promise(sample_count > 0);
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promise(max_angular_steps > 0);
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alignas(ASTCENC_VECALIGN) int isamplev[BLOCK_MAX_WEIGHTS] { 0 };
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// Precompute isample; arrays are always allocated 64 elements long
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for (unsigned int i = 0; i < sample_count; i += ASTCENC_SIMD_WIDTH)
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{
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// Add 2^23 and interpreting bits extracts round-to-nearest int
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vfloat sample = loada(samples + i) * (SINCOS_STEPS - 1.0f) + vfloat(12582912.0f);
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vint isample = float_as_int(sample) & vint((SINCOS_STEPS - 1));
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storea(isample, isamplev + i);
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}
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// Arrays are multiple of SIMD width (ANGULAR_STEPS), safe to overshoot max
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vfloat mult = vfloat(1.0f / (2.0f * astc::PI));
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for (unsigned int i = 0; i < max_angular_steps; i += ASTCENC_SIMD_WIDTH)
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{
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vfloat anglesum_x = vfloat::zero();
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vfloat anglesum_y = vfloat::zero();
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for (unsigned int j = 0; j < sample_count; j++)
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{
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int isample = isamplev[j];
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vfloat sample_weightv(sample_weights[j]);
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anglesum_x += loada(cos_table[isample] + i) * sample_weightv;
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anglesum_y += loada(sin_table[isample] + i) * sample_weightv;
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}
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vfloat angle = atan2(anglesum_y, anglesum_x);
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vfloat ofs = angle * mult;
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storea(ofs, offsets + i);
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}
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}
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/**
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* @brief For a given step size compute the lowest and highest weight.
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*
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* Compute the lowest and highest weight that results from quantizing using the given stepsize and
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* offset, and then compute the resulting error. The cut errors indicate the error that results from
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* forcing samples that should have had one weight value one step up or down.
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*
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* @param sample_count The number of samples.
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* @param samples The sample data.
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* @param sample_weights The weight of each sample.
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* @param max_angular_steps The maximum number of steps to be tested.
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* @param max_quant_steps The maximum quantization level to be tested.
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* @param offsets The angular offsets array.
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* @param[out] lowest_weight Per angular step, the lowest weight.
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* @param[out] weight_span Per angular step, the span between lowest and highest weight.
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* @param[out] error Per angular step, the error.
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* @param[out] cut_low_weight_error Per angular step, the low weight cut error.
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* @param[out] cut_high_weight_error Per angular step, the high weight cut error.
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*/
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static void compute_lowest_and_highest_weight(
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unsigned int sample_count,
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const float* samples,
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const float* sample_weights,
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unsigned int max_angular_steps,
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unsigned int max_quant_steps,
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const float* offsets,
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int* lowest_weight,
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int* weight_span,
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float* error,
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float* cut_low_weight_error,
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float* cut_high_weight_error
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) {
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promise(sample_count > 0);
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promise(max_angular_steps > 0);
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vfloat rcp_stepsize = vfloat::lane_id() + vfloat(1.0f);
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// Arrays are ANGULAR_STEPS long, so always safe to run full vectors
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for (unsigned int sp = 0; sp < max_angular_steps; sp += ASTCENC_SIMD_WIDTH)
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{
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vint minidx(128);
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vint maxidx(-128);
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vfloat errval = vfloat::zero();
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vfloat cut_low_weight_err = vfloat::zero();
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vfloat cut_high_weight_err = vfloat::zero();
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vfloat offset = loada(&offsets[sp]);
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for (unsigned int j = 0; j < sample_count; ++j)
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{
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vfloat wt = load1(&sample_weights[j]);
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vfloat sval = load1(&samples[j]) * rcp_stepsize - offset;
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vfloat svalrte = round(sval);
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vint idxv = float_to_int(svalrte);
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vfloat dif = sval - svalrte;
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vfloat dwt = dif * wt;
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errval += dwt * dif;
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// Reset tracker on min hit
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vmask mask = idxv < minidx;
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minidx = select(minidx, idxv, mask);
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cut_low_weight_err = select(cut_low_weight_err, vfloat::zero(), mask);
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// Accumulate on min hit
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mask = idxv == minidx;
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vfloat accum = cut_low_weight_err + wt - vfloat(2.0f) * dwt;
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cut_low_weight_err = select(cut_low_weight_err, accum, mask);
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// Reset tracker on max hit
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mask = idxv > maxidx;
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maxidx = select(maxidx, idxv, mask);
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cut_high_weight_err = select(cut_high_weight_err, vfloat::zero(), mask);
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// Accumulate on max hit
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mask = idxv == maxidx;
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accum = cut_high_weight_err + wt + vfloat(2.0f) * dwt;
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cut_high_weight_err = select(cut_high_weight_err, accum, mask);
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}
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// Write out min weight and weight span; clamp span to a usable range
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vint span = maxidx - minidx + vint(1);
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span = min(span, vint(max_quant_steps + 3));
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span = max(span, vint(2));
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storea(minidx, &lowest_weight[sp]);
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storea(span, &weight_span[sp]);
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// The cut_(lowest/highest)_weight_error indicate the error that results from forcing
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// samples that should have had the weight value one step (up/down).
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vfloat ssize = 1.0f / rcp_stepsize;
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vfloat errscale = ssize * ssize;
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storea(errval * errscale, &error[sp]);
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storea(cut_low_weight_err * errscale, &cut_low_weight_error[sp]);
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storea(cut_high_weight_err * errscale, &cut_high_weight_error[sp]);
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rcp_stepsize = rcp_stepsize + vfloat(ASTCENC_SIMD_WIDTH);
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}
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}
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/**
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* @brief The main function for the angular algorithm.
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*
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* @param sample_count The number of samples.
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* @param samples The sample data.
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* @param sample_weights The weight of each sample.
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* @param max_quant_level The maximum quantization level to be tested.
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* @param[out] low_value Per angular step, the lowest weight value.
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* @param[out] high_value Per angular step, the highest weight value.
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*/
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static void compute_angular_endpoints_for_quant_levels(
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unsigned int sample_count,
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const float* samples,
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const float* sample_weights,
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unsigned int max_quant_level,
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float low_value[12],
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float high_value[12]
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) {
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unsigned int max_quant_steps = quantization_steps_for_level[max_quant_level];
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alignas(ASTCENC_VECALIGN) float angular_offsets[ANGULAR_STEPS];
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unsigned int max_angular_steps = max_angular_steps_needed_for_quant_level[max_quant_level];
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compute_angular_offsets(sample_count, samples, sample_weights, max_angular_steps, angular_offsets);
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alignas(ASTCENC_VECALIGN) int32_t lowest_weight[ANGULAR_STEPS];
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alignas(ASTCENC_VECALIGN) int32_t weight_span[ANGULAR_STEPS];
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alignas(ASTCENC_VECALIGN) float error[ANGULAR_STEPS];
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alignas(ASTCENC_VECALIGN) float cut_low_weight_error[ANGULAR_STEPS];
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alignas(ASTCENC_VECALIGN) float cut_high_weight_error[ANGULAR_STEPS];
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compute_lowest_and_highest_weight(sample_count, samples, sample_weights,
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max_angular_steps, max_quant_steps,
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angular_offsets, lowest_weight, weight_span, error,
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cut_low_weight_error, cut_high_weight_error);
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// For each quantization level, find the best error terms. Use packed vectors so data-dependent
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// branches can become selects. This involves some integer to float casts, but the values are
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// small enough so they never round the wrong way.
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vfloat4 best_results[40];
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// Initialize the array to some safe defaults
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promise(max_quant_steps > 0);
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for (unsigned int i = 0; i < (max_quant_steps + 4); i++)
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{
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// Lane<0> = Best error
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// Lane<1> = Best scale; -1 indicates no solution found
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// Lane<2> = Cut low weight
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best_results[i] = vfloat4(1e30f, -1.0f, 0.0f, 0.0f);
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}
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promise(max_angular_steps > 0);
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for (unsigned int i = 0; i < max_angular_steps; i++)
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{
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int idx_span = weight_span[i];
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float error_cut_low = error[i] + cut_low_weight_error[i];
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float error_cut_high = error[i] + cut_high_weight_error[i];
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float error_cut_low_high = error[i] + cut_low_weight_error[i] + cut_high_weight_error[i];
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vfloat4 best_result;
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vfloat4 new_result;
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// Check best error against record N
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best_result = best_results[idx_span];
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new_result = vfloat4(error[i], (float)i, 0.0f, 0.0f);
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vmask4 mask1(best_result.lane<0>() > error[i]);
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best_results[idx_span] = select(best_result, new_result, mask1);
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// Check best error against record N-1 with both cut low and cut high
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best_result = best_results[idx_span - 1];
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new_result = vfloat4(error_cut_low, (float)i, 1.0f, 0.0f);
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vmask4 mask2(best_result.lane<0>() > error_cut_low);
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best_result = select(best_result, new_result, mask2);
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new_result = vfloat4(error_cut_high, (float)i, 0.0f, 0.0f);
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vmask4 mask3(best_result.lane<0>() > error_cut_high);
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best_results[idx_span - 1] = select(best_result, new_result, mask3);
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// Check best error against record N-2 with cut low high
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best_result = best_results[idx_span - 2];
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new_result = vfloat4(error_cut_low_high, (float)i, 1.0f, 0.0f);
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vmask4 mask4(best_result.lane<0>() > error_cut_low_high);
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best_results[idx_span - 2] = select(best_result, new_result, mask4);
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}
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// If we get a better error for lower sample count then use the lower sample count's error for
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// the higher sample count as well.
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for (unsigned int i = 3; i <= max_quant_steps; i++)
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{
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vfloat4 result = best_results[i];
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vfloat4 prev_result = best_results[i - 1];
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vmask4 mask(result.lane<0>() > prev_result.lane<0>());
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best_results[i] = select(result, prev_result, mask);
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}
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for (unsigned int i = 0; i <= max_quant_level; i++)
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{
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unsigned int q = quantization_steps_for_level[i];
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int bsi = (int)best_results[q].lane<1>();
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// Did we find anything?
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// TODO: Can we do better than bsi = 0 here. We should at least propagate an error?
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#if !defined(NDEBUG)
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if (bsi < 0)
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{
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printf("WARNING: Unable to find encoding within specified error limit\n");
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bsi = 0;
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}
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else
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bsi = astc::max(0, bsi);
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#endif
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float stepsize = 1.0f / (1.0f + (float)bsi);
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int lwi = lowest_weight[bsi] + (int)best_results[q].lane<2>();
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int hwi = lwi + q - 1;
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float offset = angular_offsets[bsi] * stepsize;
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low_value[i] = offset + static_cast<float>(lwi) * stepsize;
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high_value[i] = offset + static_cast<float>(hwi) * stepsize;
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}
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}
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/* See header for documentation. */
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void compute_angular_endpoints_1plane(
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bool only_always,
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const block_size_descriptor& bsd,
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const float* decimated_quantized_weights,
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const float* decimated_weights,
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float low_value[WEIGHTS_MAX_BLOCK_MODES],
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float high_value[WEIGHTS_MAX_BLOCK_MODES]
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) {
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float low_values[WEIGHTS_MAX_DECIMATION_MODES][12];
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float high_values[WEIGHTS_MAX_DECIMATION_MODES][12];
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promise(bsd.decimation_mode_count > 0);
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for (unsigned int i = 0; i < bsd.decimation_mode_count; i++)
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{
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const decimation_mode& dm = bsd.decimation_modes[i];
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if (dm.maxprec_1plane < 0 || (only_always && !dm.percentile_always) || !dm.percentile_hit)
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{
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continue;
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}
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int sample_count = bsd.decimation_tables[i]->weight_count;
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compute_angular_endpoints_for_quant_levels(
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sample_count,
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decimated_quantized_weights + i * BLOCK_MAX_WEIGHTS,
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decimated_weights + i * BLOCK_MAX_WEIGHTS,
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dm.maxprec_1plane, low_values[i], high_values[i]);
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}
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promise(bsd.block_mode_count > 0);
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for (unsigned int i = 0; i < bsd.block_mode_count; ++i)
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{
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const block_mode& bm = bsd.block_modes[i];
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if (bm.is_dual_plane || (only_always && !bm.percentile_always) || !bm.percentile_hit)
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{
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continue;
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}
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unsigned int quant_mode = bm.quant_mode;
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unsigned int decim_mode = bm.decimation_mode;
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low_value[i] = low_values[decim_mode][quant_mode];
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high_value[i] = high_values[decim_mode][quant_mode];
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}
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}
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/* See header for documentation. */
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void compute_angular_endpoints_2planes(
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const block_size_descriptor& bsd,
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const float* decimated_quantized_weights,
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const float* decimated_weights,
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float low_value1[WEIGHTS_MAX_BLOCK_MODES],
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float high_value1[WEIGHTS_MAX_BLOCK_MODES],
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float low_value2[WEIGHTS_MAX_BLOCK_MODES],
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float high_value2[WEIGHTS_MAX_BLOCK_MODES]
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) {
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float low_values1[WEIGHTS_MAX_DECIMATION_MODES][12];
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float high_values1[WEIGHTS_MAX_DECIMATION_MODES][12];
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float low_values2[WEIGHTS_MAX_DECIMATION_MODES][12];
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float high_values2[WEIGHTS_MAX_DECIMATION_MODES][12];
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promise(bsd.decimation_mode_count > 0);
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for (unsigned int i = 0; i < bsd.decimation_mode_count; i++)
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{
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const decimation_mode& dm = bsd.decimation_modes[i];
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if (dm.maxprec_2planes < 0 || !dm.percentile_hit)
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{
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continue;
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}
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unsigned int sample_count = bsd.decimation_tables[i]->weight_count;
|
|
|
|
compute_angular_endpoints_for_quant_levels(
|
|
sample_count,
|
|
decimated_quantized_weights + 2 * i * BLOCK_MAX_WEIGHTS,
|
|
decimated_weights + 2 * i * BLOCK_MAX_WEIGHTS,
|
|
dm.maxprec_2planes, low_values1[i], high_values1[i]);
|
|
|
|
compute_angular_endpoints_for_quant_levels(
|
|
sample_count,
|
|
decimated_quantized_weights + (2 * i + 1) * BLOCK_MAX_WEIGHTS,
|
|
decimated_weights + (2 * i + 1) * BLOCK_MAX_WEIGHTS,
|
|
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
|