Reduce the amount of computation in combine_two_samples().

[movit] / resample_effect.cpp

// Three-lobed Lanczos, the most common choice.
#define LANCZOS_RADIUS 3.0

#include <epoxy/gl.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <algorithm>
#include <Eigen/Sparse>
#include <Eigen/SparseQR>
#include <Eigen/OrderingMethods>

#include "effect_chain.h"
#include "effect_util.h"
#include "fp16.h"
#include "init.h"
#include "resample_effect.h"
#include "util.h"

using namespace Eigen;
using namespace std;

namespace movit {

namespace {

template<class T>
struct Tap {
        T weight;
        T pos;
};

float sinc(float x)
{
        if (fabs(x) < 1e-6) {
                return 1.0f - fabs(x);
        } else {
                return sin(x) / x;
        }
}

float lanczos_weight(float x, float a)
{
        if (fabs(x) > a) {
                return 0.0f;
        } else {
                return sinc(M_PI * x) * sinc(M_PI * x / a);
        }
}

// Euclid's algorithm, from Wikipedia.
unsigned gcd(unsigned a, unsigned b)
{
        while (b != 0) {
                unsigned t = b;
                b = a % b;
                a = t;
        }
        return a;
}

template<class DestFloat>
unsigned combine_samples(const Tap<float> *src, Tap<DestFloat> *dst, float num_subtexels, float inv_num_subtexels, unsigned num_src_samples, unsigned max_samples_saved)
{
        // Cut off near-zero values at both sides.
        unsigned num_samples_saved = 0;
        while (num_samples_saved < max_samples_saved &&
               num_src_samples > 0 &&
               fabs(src[0].weight) < 1e-6) {
                ++src;
                --num_src_samples;
                ++num_samples_saved;
        }
        while (num_samples_saved < max_samples_saved &&
               num_src_samples > 0 &&
               fabs(src[num_src_samples - 1].weight) < 1e-6) {
                --num_src_samples;
                ++num_samples_saved;
        }

        for (unsigned i = 0, j = 0; i < num_src_samples; ++i, ++j) {
                // Copy the sample directly; it will be overwritten later if we can combine.
                if (dst != NULL) {
                        dst[j].weight = convert_float<float, DestFloat>(src[i].weight);
                        dst[j].pos = convert_float<float, DestFloat>(src[i].pos);
                }

                if (i == num_src_samples - 1) {
                        // Last sample; cannot combine.
                        continue;
                }
                assert(num_samples_saved <= max_samples_saved);
                if (num_samples_saved == max_samples_saved) {
                        // We could maybe save more here, but other rows can't, so don't bother.
                        continue;
                }

                float w1 = src[i].weight;
                float w2 = src[i + 1].weight;
                if (w1 * w2 < 0.0f) {
                        // Differing signs; cannot combine.
                        continue;
                }

                float pos1 = src[i].pos;
                float pos2 = src[i + 1].pos;
                assert(pos2 > pos1);

                fp16_int_t pos, total_weight;
                float sum_sq_error;
                combine_two_samples(w1, w2, pos1, pos2, num_subtexels, inv_num_subtexels, &pos, &total_weight, &sum_sq_error);

                // If the interpolation error is larger than that of about sqrt(2) of
                // a level at 8-bit precision, don't combine. (You'd think 1.0 was enough,
                // but since the artifacts are not really random, they can get quite
                // visible. On the other hand, going to 0.25f, I can see no change at
                // all with 8-bit output, so it would not seem to be worth it.)
                if (sum_sq_error > 0.5f / (255.0f * 255.0f)) {
                        continue;
                }

                // OK, we can combine this and the next sample.
                if (dst != NULL) {
                        dst[j].weight = total_weight;
                        dst[j].pos = pos;
                }

                ++i;  // Skip the next sample.
                ++num_samples_saved;
        }
        return num_samples_saved;
}

// Normalize so that the sum becomes one. Note that we do it twice;
// this sometimes helps a tiny little bit when we have many samples.
template<class T>
void normalize_sum(Tap<T>* vals, unsigned num)
{
        for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) {
                double sum = 0.0;
                for (unsigned i = 0; i < num; ++i) {
                        sum += to_fp64(vals[i].weight);
                }
                for (unsigned i = 0; i < num; ++i) {
                        vals[i].weight = from_fp64<T>(to_fp64(vals[i].weight) / sum);
                }
        }
}

// Make use of the bilinear filtering in the GPU to reduce the number of samples
// we need to make. This is a bit more complex than BlurEffect since we cannot combine
// two neighboring samples if their weights have differing signs, so we first need to
// figure out the maximum number of samples. Then, we downconvert all the weights to
// that number -- we could have gone for a variable-length system, but this is simpler,
// and the gains would probably be offset by the extra cost of checking when to stop.
//
// The greedy strategy for combining samples is optimal.
template<class DestFloat>
unsigned combine_many_samples(const Tap<float> *weights, unsigned src_size, unsigned src_samples, unsigned dst_samples, Tap<DestFloat> **bilinear_weights)
{
        float num_subtexels = src_size / movit_texel_subpixel_precision;
        float inv_num_subtexels = movit_texel_subpixel_precision / src_size;
        int src_bilinear_samples = 0;

        for (unsigned y = 0; y < dst_samples; ++y) {
                unsigned num_samples_saved = combine_samples<DestFloat>(weights + y * src_samples, NULL, num_subtexels, inv_num_subtexels, src_samples, UINT_MAX);
                src_bilinear_samples = max<int>(src_bilinear_samples, src_samples - num_samples_saved);
        }

        // Now that we know the right width, actually combine the samples.
        *bilinear_weights = new Tap<DestFloat>[dst_samples * src_bilinear_samples];
        for (unsigned y = 0; y < dst_samples; ++y) {
                Tap<DestFloat> *bilinear_weights_ptr = *bilinear_weights + y * src_bilinear_samples;
                unsigned num_samples_saved = combine_samples(
                        weights + y * src_samples,
                        bilinear_weights_ptr,
                        num_subtexels,
                        inv_num_subtexels,
                        src_samples,
                        src_samples - src_bilinear_samples);
                assert(int(src_samples) - int(num_samples_saved) == src_bilinear_samples);
                normalize_sum(bilinear_weights_ptr, src_bilinear_samples);
        }
        return src_bilinear_samples;
}

// Compute the sum of squared errors between the ideal weights (which are
// assumed to fall exactly on pixel centers) and the weights that result
// from sampling at <bilinear_weights>. The primary reason for the difference
// is inaccuracy in the sampling positions, both due to limited precision
// in storing them (already inherent in sending them in as fp16_int_t)
// and in subtexel sampling precision (which we calculate in this function).
template<class T>
double compute_sum_sq_error(const Tap<float>* weights, unsigned num_weights,
                            const Tap<T>* bilinear_weights, unsigned num_bilinear_weights,
                            unsigned size)
{
        // Find the effective range of the bilinear-optimized kernel.
        // Due to rounding of the positions, this is not necessarily the same
        // as the intended range (ie., the range of the original weights).
        int lower_pos = int(floor(to_fp64(bilinear_weights[0].pos) * size - 0.5));
        int upper_pos = int(ceil(to_fp64(bilinear_weights[num_bilinear_weights - 1].pos) * size - 0.5)) + 2;
        lower_pos = min<int>(lower_pos, lrintf(weights[0].pos * size - 0.5));
        upper_pos = max<int>(upper_pos, lrintf(weights[num_weights - 1].pos * size - 0.5) + 1);

        float* effective_weights = new float[upper_pos - lower_pos];
        for (int i = 0; i < upper_pos - lower_pos; ++i) {
                effective_weights[i] = 0.0f;
        }

        // Now find the effective weights that result from this sampling.
        for (unsigned i = 0; i < num_bilinear_weights; ++i) {
                const float pixel_pos = to_fp64(bilinear_weights[i].pos) * size - 0.5f;
                const int x0 = int(floor(pixel_pos)) - lower_pos;
                const int x1 = x0 + 1;
                const float f = lrintf((pixel_pos - (x0 + lower_pos)) / movit_texel_subpixel_precision) * movit_texel_subpixel_precision;

                assert(x0 >= 0);
                assert(x1 >= 0);
                assert(x0 < upper_pos - lower_pos);
                assert(x1 < upper_pos - lower_pos);

                effective_weights[x0] += to_fp64(bilinear_weights[i].weight) * (1.0 - f);
                effective_weights[x1] += to_fp64(bilinear_weights[i].weight) * f;
        }

        // Subtract the desired weights to get the error.
        for (unsigned i = 0; i < num_weights; ++i) {
                const int x = lrintf(weights[i].pos * size - 0.5f) - lower_pos;
                assert(x >= 0);
                assert(x < upper_pos - lower_pos);

                effective_weights[x] -= weights[i].weight;
        }

        double sum_sq_error = 0.0;
        for (unsigned i = 0; i < num_weights; ++i) {
                sum_sq_error += effective_weights[i] * effective_weights[i];
        }

        delete[] effective_weights;
        return sum_sq_error;
}

}  // namespace

ResampleEffect::ResampleEffect()
        : input_width(1280),
          input_height(720),
          offset_x(0.0f), offset_y(0.0f),
          zoom_x(1.0f), zoom_y(1.0f),
          zoom_center_x(0.5f), zoom_center_y(0.5f)
{
        register_int("width", &output_width);
        register_int("height", &output_height);

        // The first blur pass will forward resolution information to us.
        hpass = new SingleResamplePassEffect(this);
        CHECK(hpass->set_int("direction", SingleResamplePassEffect::HORIZONTAL));
        vpass = new SingleResamplePassEffect(NULL);
        CHECK(vpass->set_int("direction", SingleResamplePassEffect::VERTICAL));

        update_size();
}

void ResampleEffect::rewrite_graph(EffectChain *graph, Node *self)
{
        Node *hpass_node = graph->add_node(hpass);
        Node *vpass_node = graph->add_node(vpass);
        graph->connect_nodes(hpass_node, vpass_node);
        graph->replace_receiver(self, hpass_node);
        graph->replace_sender(self, vpass_node);
        self->disabled = true;
} 

// We get this information forwarded from the first blur pass,
// since we are not part of the chain ourselves.
void ResampleEffect::inform_input_size(unsigned input_num, unsigned width, unsigned height)
{
        assert(input_num == 0);
        assert(width != 0);
        assert(height != 0);
        input_width = width;
        input_height = height;
        update_size();
}

void ResampleEffect::update_size()
{
        bool ok = true;
        ok |= hpass->set_int("input_width", input_width);
        ok |= hpass->set_int("input_height", input_height);
        ok |= hpass->set_int("output_width", output_width);
        ok |= hpass->set_int("output_height", input_height);

        ok |= vpass->set_int("input_width", output_width);
        ok |= vpass->set_int("input_height", input_height);
        ok |= vpass->set_int("output_width", output_width);
        ok |= vpass->set_int("output_height", output_height);

        assert(ok);

        // The offset added due to zoom may have changed with the size.
        update_offset_and_zoom();
}

void ResampleEffect::update_offset_and_zoom()
{
        bool ok = true;

        // Zoom from the right origin. (zoom_center is given in normalized coordinates,
        // i.e. 0..1.)
        float extra_offset_x = zoom_center_x * (1.0f - 1.0f / zoom_x) * input_width;
        float extra_offset_y = (1.0f - zoom_center_y) * (1.0f - 1.0f / zoom_y) * input_height;

        ok |= hpass->set_float("offset", extra_offset_x + offset_x);
        ok |= vpass->set_float("offset", extra_offset_y - offset_y);  // Compensate for the bottom-left origin.
        ok |= hpass->set_float("zoom", zoom_x);
        ok |= vpass->set_float("zoom", zoom_y);

        assert(ok);
}

bool ResampleEffect::set_float(const string &key, float value) {
        if (key == "width") {
                output_width = value;
                update_size();
                return true;
        }
        if (key == "height") {
                output_height = value;
                update_size();
                return true;
        }
        if (key == "top") {
                offset_y = value;
                update_offset_and_zoom();
                return true;
        }
        if (key == "left") {
                offset_x = value;
                update_offset_and_zoom();
                return true;
        }
        if (key == "zoom_x") {
                if (value <= 0.0f) {
                        return false;
                }
                zoom_x = value;
                update_offset_and_zoom();
                return true;
        }
        if (key == "zoom_y") {
                if (value <= 0.0f) {
                        return false;
                }
                zoom_y = value;
                update_offset_and_zoom();
                return true;
        }
        if (key == "zoom_center_x") {
                zoom_center_x = value;
                update_offset_and_zoom();
                return true;
        }
        if (key == "zoom_center_y") {
                zoom_center_y = value;
                update_offset_and_zoom();
                return true;
        }
        return false;
}

SingleResamplePassEffect::SingleResamplePassEffect(ResampleEffect *parent)
        : parent(parent),
          direction(HORIZONTAL),
          input_width(1280),
          input_height(720),
          offset(0.0),
          zoom(1.0),
          last_input_width(-1),
          last_input_height(-1),
          last_output_width(-1),
          last_output_height(-1),
          last_offset(0.0 / 0.0),  // NaN.
          last_zoom(0.0 / 0.0),  // NaN.
          last_texture_width(-1), last_texture_height(-1)
{
        register_int("direction", (int *)&direction);
        register_int("input_width", &input_width);
        register_int("input_height", &input_height);
        register_int("output_width", &output_width);
        register_int("output_height", &output_height);
        register_float("offset", &offset);
        register_float("zoom", &zoom);
        register_uniform_sampler2d("sample_tex", &uniform_sample_tex);
        register_uniform_int("num_samples", &uniform_num_samples);  // FIXME: What about GLSL pre-1.30?
        register_uniform_float("num_loops", &uniform_num_loops);
        register_uniform_float("slice_height", &uniform_slice_height);
        register_uniform_float("sample_x_scale", &uniform_sample_x_scale);
        register_uniform_float("sample_x_offset", &uniform_sample_x_offset);
        register_uniform_float("whole_pixel_offset", &uniform_whole_pixel_offset);

        glGenTextures(1, &texnum);
}

SingleResamplePassEffect::~SingleResamplePassEffect()
{
        glDeleteTextures(1, &texnum);
}

string SingleResamplePassEffect::output_fragment_shader()
{
        char buf[256];
        sprintf(buf, "#define DIRECTION_VERTICAL %d\n", (direction == VERTICAL));
        return buf + read_file("resample_effect.frag");
}

// Using vertical scaling as an example:
//
// Generally out[y] = w0 * in[yi] + w1 * in[yi + 1] + w2 * in[yi + 2] + ...
//
// Obviously, yi will depend on y (in a not-quite-linear way), but so will
// the weights w0, w1, w2, etc.. The easiest way of doing this is to encode,
// for each sample, the weight and the yi value, e.g. <yi, w0>, <yi + 1, w1>,
// and so on. For each y, we encode these along the x-axis (since that is spare),
// so out[0] will read from parameters <x,y> = <0,0>, <1,0>, <2,0> and so on.
//
// For horizontal scaling, we fill in the exact same texture;
// the shader just interprets it differently.
void SingleResamplePassEffect::update_texture(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
{
        unsigned src_size, dst_size;
        if (direction == SingleResamplePassEffect::HORIZONTAL) {
                assert(input_height == output_height);
                src_size = input_width;
                dst_size = output_width;
        } else if (direction == SingleResamplePassEffect::VERTICAL) {
                assert(input_width == output_width);
                src_size = input_height;
                dst_size = output_height;
        } else {
                assert(false);
        }

        // For many resamplings (e.g. 640 -> 1280), we will end up with the same
        // set of samples over and over again in a loop. Thus, we can compute only
        // the first such loop, and then ask the card to repeat the texture for us.
        // This is both easier on the texture cache and lowers our CPU cost for
        // generating the kernel somewhat.
        float scaling_factor;
        if (fabs(zoom - 1.0f) < 1e-6) {
                num_loops = gcd(src_size, dst_size);
                scaling_factor = float(dst_size) / float(src_size);
        } else {
                // If zooming is enabled (ie., zoom != 1), we turn off the looping.
                // We _could_ perhaps do it for rational zoom levels (especially
                // things like 2:1), but it doesn't seem to be worth it, given that
                // the most common use case would seem to be varying the zoom
                // from frame to frame.
                num_loops = 1;
                scaling_factor = zoom * float(dst_size) / float(src_size);
        }
        slice_height = 1.0f / num_loops;
        unsigned dst_samples = dst_size / num_loops;

        // Sample the kernel in the right place. A diagram with a triangular kernel
        // (corresponding to linear filtering, and obviously with radius 1)
        // for easier ASCII art drawing:
        //
        //                *
        //               / \                      |
        //              /   \                     |
        //             /     \                    |
        //    x---x---x   x   x---x---x---x
        //
        // Scaling up (in this case, 2x) means sampling more densely:
        //
        //                *
        //               / \                      |
        //              /   \                     |
        //             /     \                    |
        //   x-x-x-x-x-x x x x-x-x-x-x-x-x-x
        //
        // When scaling up, any destination pixel will only be influenced by a few
        // (in this case, two) neighboring pixels, and more importantly, the number
        // will not be influenced by the scaling factor. (Note, however, that the
        // pixel centers have moved, due to OpenGL's center-pixel convention.)
        // The only thing that changes is the weights themselves, as the sampling
        // points are at different distances from the original pixels.
        //
        // Scaling down is a different story:
        //
        //                *
        //               / \                      |
        //              /   \                     |
        //             /     \                    |
        //    --x------ x     --x-------x--
        //
        // Again, the pixel centers have moved in a maybe unintuitive fashion,
        // although when you consider that there are multiple source pixels around,
        // it's not so bad as at first look:
        //
        //            *   *   *   *
        //           / \ / \ / \ / \              |
        //          /   X   X   X   \             |
        //         /   / \ / \ / \   \            |
        //    --x-------x-------x-------x--
        //
        // As you can see, the new pixels become averages of the two neighboring old
        // ones (the situation for Lanczos is of course more complex).
        //
        // Anyhow, in this case we clearly need to look at more source pixels
        // to compute the destination pixel, and how many depend on the scaling factor.
        // Thus, the kernel width will vary with how much we scale.
        float radius_scaling_factor = min(scaling_factor, 1.0f);
        int int_radius = lrintf(LANCZOS_RADIUS / radius_scaling_factor);
        int src_samples = int_radius * 2 + 1;
        Tap<float> *weights = new Tap<float>[dst_samples * src_samples];
        float subpixel_offset = offset - lrintf(offset);  // The part not covered by whole_pixel_offset.
        assert(subpixel_offset >= -0.5f && subpixel_offset <= 0.5f);
        for (unsigned y = 0; y < dst_samples; ++y) {
                // Find the point around which we want to sample the source image,
                // compensating for differing pixel centers as the scale changes.
                float center_src_y = (y + 0.5f) / scaling_factor - 0.5f;
                int base_src_y = lrintf(center_src_y);

                // Now sample <int_radius> pixels on each side around that point.
                for (int i = 0; i < src_samples; ++i) {
                        int src_y = base_src_y + i - int_radius;
                        float weight = lanczos_weight(radius_scaling_factor * (src_y - center_src_y - subpixel_offset), LANCZOS_RADIUS);
                        weights[y * src_samples + i].weight = weight * radius_scaling_factor;
                        weights[y * src_samples + i].pos = (src_y + 0.5) / float(src_size);
                }
        }

        // Now make use of the bilinear filtering in the GPU to reduce the number of samples
        // we need to make. Try fp16 first; if it's not accurate enough, we go to fp32.
        // Our tolerance level for total error is a bit higher than the one for invididual
        // samples, since one would assume overall errors in the shape don't matter as much.
        const float max_error = 2.0f / (255.0f * 255.0f);
        Tap<fp16_int_t> *bilinear_weights_fp16;
        src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp16);
        Tap<float> *bilinear_weights_fp32 = NULL;
        bool fallback_to_fp32 = false;
        double max_sum_sq_error_fp16 = 0.0;
        for (unsigned y = 0; y < dst_samples; ++y) {
                double sum_sq_error_fp16 = compute_sum_sq_error(
                        weights + y * src_samples, src_samples,
                        bilinear_weights_fp16 + y * src_bilinear_samples, src_bilinear_samples,
                        src_size);
                max_sum_sq_error_fp16 = std::max(max_sum_sq_error_fp16, sum_sq_error_fp16);
                if (max_sum_sq_error_fp16 > max_error) {
                        break;
                }
        }

        if (max_sum_sq_error_fp16 > max_error) {
                fallback_to_fp32 = true;
                src_bilinear_samples = combine_many_samples(weights, src_size, src_samples, dst_samples, &bilinear_weights_fp32);
        }

        // Encode as a two-component texture. Note the GL_REPEAT.
        glActiveTexture(GL_TEXTURE0 + *sampler_num);
        check_error();
        glBindTexture(GL_TEXTURE_2D, texnum);
        check_error();
        if (last_texture_width == -1) {
                // Need to set this state the first time.
                glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
                check_error();
                glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
                check_error();
                glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
                check_error();
        }

        GLenum type, internal_format;
        void *pixels;
        if (fallback_to_fp32) {
                type = GL_FLOAT;
                internal_format = GL_RG32F;
                pixels = bilinear_weights_fp32;
        } else {
                type = GL_HALF_FLOAT;
                internal_format = GL_RG16F;
                pixels = bilinear_weights_fp16;
        }

        if (int(src_bilinear_samples) == last_texture_width &&
            int(dst_samples) == last_texture_height &&
            internal_format == last_texture_internal_format) {
                // Texture dimensions and type are unchanged; it is more efficient
                // to just update it rather than making an entirely new texture.
                glTexSubImage2D(GL_TEXTURE_2D, 0, 0, 0, src_bilinear_samples, dst_samples, GL_RG, type, pixels);
        } else {
                glTexImage2D(GL_TEXTURE_2D, 0, internal_format, src_bilinear_samples, dst_samples, 0, GL_RG, type, pixels);
                last_texture_width = src_bilinear_samples;
                last_texture_height = dst_samples;
                last_texture_internal_format = internal_format;
        }
        check_error();

        delete[] weights;
        delete[] bilinear_weights_fp16;
        delete[] bilinear_weights_fp32;
}

void SingleResamplePassEffect::set_gl_state(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
{
        Effect::set_gl_state(glsl_program_num, prefix, sampler_num);

        assert(input_width > 0);
        assert(input_height > 0);
        assert(output_width > 0);
        assert(output_height > 0);

        if (input_width != last_input_width ||
            input_height != last_input_height ||
            output_width != last_output_width ||
            output_height != last_output_height ||
            offset != last_offset ||
            zoom != last_zoom) {
                update_texture(glsl_program_num, prefix, sampler_num);
                last_input_width = input_width;
                last_input_height = input_height;
                last_output_width = output_width;
                last_output_height = output_height;
                last_offset = offset;
                last_zoom = zoom;
        }

        glActiveTexture(GL_TEXTURE0 + *sampler_num);
        check_error();
        glBindTexture(GL_TEXTURE_2D, texnum);
        check_error();

        uniform_sample_tex = *sampler_num;
        ++*sampler_num;
        uniform_num_samples = src_bilinear_samples;
        uniform_num_loops = num_loops;
        uniform_slice_height = slice_height;

        // Instructions for how to convert integer sample numbers to positions in the weight texture.
        uniform_sample_x_scale = 1.0f / src_bilinear_samples;
        uniform_sample_x_offset = 0.5f / src_bilinear_samples;

        if (direction == SingleResamplePassEffect::VERTICAL) {
                uniform_whole_pixel_offset = lrintf(offset) / float(input_height);
        } else {
                uniform_whole_pixel_offset = lrintf(offset) / float(input_width);
        }

        // We specifically do not want mipmaps on the input texture;
        // they break minification.
        Node *self = chain->find_node_for_effect(this);
        glActiveTexture(chain->get_input_sampler(self, 0));
        check_error();
        glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
        check_error();
}

}  // namespace movit