Compute version of ResampleEffect.

[movit] / resample_effect.cpp

// Three-lobed Lanczos, the most common choice.
// Note that if you change this, the accuracy for LANCZOS_TABLE_SIZE
// needs to be recomputed.
#define LANCZOS_RADIUS 3.0f

#include <epoxy/gl.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <algorithm>
#include <mutex>
#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 {

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

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

// The weight function can be expensive to compute over and over again
// (which will happen during e.g. a zoom), but it is also easy to interpolate
// linearly. We compute the right half of the function (in the range of
// 0..LANCZOS_RADIUS), with two guard elements for easier interpolation, and
// linearly interpolate to get our function.
//
// We want to scale the table so that the maximum error is always smaller
// than 1e-6. As per http://www-solar.mcs.st-andrews.ac.uk/~clare/Lectures/num-analysis/Numan_chap3.pdf,
// the error for interpolating a function linearly between points [a,b] is
//
//   e = 1/2 (x-a)(x-b) f''(u_x)
//
// for some point u_x in [a,b] (where f(x) is our Lanczos function; we're
// assuming LANCZOS_RADIUS=3 from here on). Obviously this is bounded by
// f''(x) over the entire range. Numeric optimization shows the maximum of
// |f''(x)| to be in x=1.09369819474562880, with the value 2.40067758733152381.
// So if the steps between consecutive values are called d, we get
//
//   |e| <= 1/2 (d/2)^2 2.4007
//   |e| <= 0.1367 d^2
//
// Solve for e = 1e-6 yields a step size of 0.0027, which to cover the range
// 0..3 needs 1109 steps. We round up to the next power of two, just to be sure.
//
// You need to call lanczos_table_init_done before the first call to
// lanczos_weight_cached.
#define LANCZOS_TABLE_SIZE 2048
static once_flag lanczos_table_init_done;
float lanczos_table[LANCZOS_TABLE_SIZE + 2];

void init_lanczos_table()
{
        for (unsigned i = 0; i < LANCZOS_TABLE_SIZE + 2; ++i) {
                lanczos_table[i] = lanczos_weight(float(i) * (LANCZOS_RADIUS / LANCZOS_TABLE_SIZE));
        }
}

float lanczos_weight_cached(float x)
{
        x = fabs(x);
        if (x > LANCZOS_RADIUS) {
                return 0.0f;
        }
        float table_pos = x * (LANCZOS_TABLE_SIZE / LANCZOS_RADIUS);
        unsigned table_pos_int = int(table_pos);  // Truncate towards zero.
        float table_pos_frac = table_pos - table_pos_int;
        assert(table_pos < LANCZOS_TABLE_SIZE + 2);
        return lanczos_table[table_pos_int] +
                table_pos_frac * (lanczos_table[table_pos_int + 1] - lanczos_table[table_pos_int]);
}

// 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, float pos1_pos2_diff, float inv_pos1_pos2_diff)
{
        // 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 != nullptr) {
                        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);

                DestFloat pos, total_weight;
                float sum_sq_error;
                combine_two_samples(w1, w2, pos1, pos1_pos2_diff, inv_pos1_pos2_diff, 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 != nullptr) {
                        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) {
                float sum = 0.0;
                for (unsigned i = 0; i < num; ++i) {
                        sum += to_fp32(vals[i].weight);
                }
                float inv_sum = 1.0 / sum;
                for (unsigned i = 0; i < num; ++i) {
                        vals[i].weight = from_fp32<T>(to_fp32(vals[i].weight) * inv_sum);
                }
        }
}

template<class T>
void normalize_sum(T* vals, unsigned num)
{
        for (int normalize_pass = 0; normalize_pass < 2; ++normalize_pass) {
                float sum = 0.0;
                for (unsigned i = 0; i < num; ++i) {
                        sum += to_fp32(vals[i]);
                }
                float inv_sum = 1.0 / sum;
                for (unsigned i = 0; i < num; ++i) {
                        vals[i] = from_fp32<T>(to_fp32(vals[i]) * inv_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, unique_ptr<Tap<DestFloat>[]> *bilinear_weights)
{
        float num_subtexels = src_size / movit_texel_subpixel_precision;
        float inv_num_subtexels = movit_texel_subpixel_precision / src_size;
        float pos1_pos2_diff = 1.0f / src_size;
        float inv_pos1_pos2_diff = src_size;

        unsigned max_samples_saved = UINT_MAX;
        for (unsigned y = 0; y < dst_samples && max_samples_saved > 0; ++y) {
                unsigned num_samples_saved = combine_samples<DestFloat>(weights + y * src_samples, nullptr, num_subtexels, inv_num_subtexels, src_samples, max_samples_saved, pos1_pos2_diff, inv_pos1_pos2_diff);
                max_samples_saved = min(max_samples_saved, num_samples_saved);
        }

        // Now that we know the right width, actually combine the samples.
        unsigned src_bilinear_samples = src_samples - max_samples_saved;
        bilinear_weights->reset(new Tap<DestFloat>[dst_samples * src_bilinear_samples]);
        for (unsigned y = 0; y < dst_samples; ++y) {
                Tap<DestFloat> *bilinear_weights_ptr = bilinear_weights->get() + y * src_bilinear_samples;
                unsigned num_samples_saved = combine_samples(
                        weights + y * src_samples,
                        bilinear_weights_ptr,
                        num_subtexels,
                        inv_num_subtexels,
                        src_samples,
                        max_samples_saved,
                        pos1_pos2_diff,
                        inv_pos1_pos2_diff);
                assert(num_samples_saved == max_samples_saved);
                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_fp32(bilinear_weights[0].pos) * size - 0.5f));
        int upper_pos = int(ceil(to_fp32(bilinear_weights[num_bilinear_weights - 1].pos) * size - 0.5f)) + 2;
        lower_pos = min<int>(lower_pos, lrintf(weights[0].pos * size - 0.5f));
        upper_pos = max<int>(upper_pos, lrintf(weights[num_weights - 1].pos * size - 0.5f) + 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_fp32(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_fp32(bilinear_weights[i].weight) * (1.0f - f);
                effective_weights[x1] += to_fp32(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);

        if (movit_compute_shaders_supported) {
                // The effect will forward resolution information to us.
                compute_effect_owner.reset(new ResampleComputeEffect(this));
                compute_effect = compute_effect_owner.get();
        } else {
                // The first blur pass will forward resolution information to us.
                hpass_owner.reset(new SingleResamplePassEffect(this));
                hpass = hpass_owner.get();
                CHECK(hpass->set_int("direction", SingleResamplePassEffect::HORIZONTAL));
                vpass_owner.reset(new SingleResamplePassEffect(this));
                vpass = vpass_owner.get();
                CHECK(vpass->set_int("direction", SingleResamplePassEffect::VERTICAL));
        }

        update_size();
}

ResampleEffect::~ResampleEffect()
{
}

void ResampleEffect::rewrite_graph(EffectChain *graph, Node *self)
{
        if (compute_effect != nullptr) {
                Node *compute_node = graph->add_node(compute_effect_owner.release());
                graph->replace_receiver(self, compute_node);
                graph->replace_sender(self, compute_node);
        } else {
                Node *hpass_node = graph->add_node(hpass_owner.release());
                Node *vpass_node = graph->add_node(vpass_owner.release());
                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;
        if (compute_effect != nullptr) {
                ok |= compute_effect->set_int("input_width", input_width);
                ok |= compute_effect->set_int("input_height", input_height);
                ok |= compute_effect->set_int("output_width", output_width);
                ok |= compute_effect->set_int("output_height", output_height);
        } else {
                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;

        if (compute_effect != nullptr) {
                ok |= compute_effect->set_float("offset_x", extra_offset_x + offset_x);
                ok |= compute_effect->set_float("offset_y", extra_offset_y - offset_y);  // Compensate for the bottom-left origin.
                ok |= compute_effect->set_float("zoom_x", zoom_x);
                ok |= compute_effect->set_float("zoom_y", zoom_y);
        } else {
                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.
{
        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);
        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);

        call_once(lanczos_table_init_done, init_lanczos_table);
}

SingleResamplePassEffect::~SingleResamplePassEffect()
{
}

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);
        }

        ScalingWeights weights = calculate_bilinear_scaling_weights(src_size, dst_size, zoom, offset, BilinearFormatConstraints::ALLOW_FP16_AND_FP32);
        src_bilinear_samples = weights.src_bilinear_samples;
        num_loops = weights.num_loops;
        slice_height = 1.0f / weights.num_loops;

        // Encode as a two-component texture. Note the GL_REPEAT.
        glActiveTexture(GL_TEXTURE0 + *sampler_num);
        check_error();
        glBindTexture(GL_TEXTURE_2D, tex.get_texnum());
        check_error();

        GLenum type, internal_format;
        void *pixels;
        assert((weights.bilinear_weights_fp16 == nullptr) != (weights.bilinear_weights_fp32 == nullptr));
        if (weights.bilinear_weights_fp32 != nullptr) {
                type = GL_FLOAT;
                internal_format = GL_RG32F;
                pixels = weights.bilinear_weights_fp32.get();
        } else {
                type = GL_HALF_FLOAT;
                internal_format = GL_RG16F;
                pixels = weights.bilinear_weights_fp16.get();
        }

        tex.update(weights.src_bilinear_samples, weights.dst_samples, internal_format, GL_RG, type, pixels);
}

ResampleComputeEffect::ResampleComputeEffect(ResampleEffect *parent)
        : parent(parent),
          input_width(1280),
          input_height(720),
          offset_x(0.0),
          offset_y(0.0),
          zoom_x(1.0),
          zoom_y(1.0),
          last_input_width(-1),
          last_input_height(-1),
          last_output_width(-1),
          last_output_height(-1),
          last_offset_x(0.0 / 0.0),  // NaN.
          last_offset_y(0.0 / 0.0),  // NaN.
          last_zoom_x(0.0 / 0.0),  // NaN.
          last_zoom_y(0.0 / 0.0)  // NaN.
{
        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_x", &offset_x);
        register_float("offset_y", &offset_y);
        register_float("zoom_x", &zoom_x);
        register_float("zoom_y", &zoom_y);
        register_uniform_sampler2d("sample_tex_horizontal", &uniform_sample_tex_horizontal);
        register_uniform_sampler2d("sample_tex_vertical", &uniform_sample_tex_vertical);
        register_uniform_int("num_horizontal_samples", &uniform_num_horizontal_samples);
        register_uniform_int("num_vertical_samples", &uniform_num_vertical_samples);
        register_uniform_int("vertical_int_radius", &uniform_vertical_int_radius);
        register_uniform_float("inv_vertical_scaling_factor", &uniform_inv_vertical_scaling_factor);
        register_uniform_int("output_samples_per_block", &uniform_output_samples_per_block);
        register_uniform_int("num_horizontal_filters", &uniform_num_horizontal_filters);
        register_uniform_int("num_vertical_filters", &uniform_num_vertical_filters);
        register_uniform_float("slice_height", &uniform_slice_height);
        register_uniform_float("horizontal_whole_pixel_offset", &uniform_horizontal_whole_pixel_offset);
        register_uniform_int("vertical_whole_pixel_offset", &uniform_vertical_whole_pixel_offset);
        register_uniform_float("inv_input_height", &uniform_inv_input_height);
        register_uniform_float("input_texcoord_y_adjust", &uniform_input_texcoord_y_adjust);

        call_once(lanczos_table_init_done, init_lanczos_table);
}

ResampleComputeEffect::~ResampleComputeEffect()
{
}

string ResampleComputeEffect::output_fragment_shader()
{
        char buf[256] = "";
        return buf + read_file("resample_effect.comp");
}

// The compute shader does horizontal scaling first, using exactly the same
// two-component texture format as in the two-pass version (see the comments
// on ResampleComputeEffect). The vertical scaling calculates the offset values
// in the shader, so we only store a one-component texture with the weights
// for each filter.
void ResampleComputeEffect::update_texture(GLuint glsl_program_num, const string &prefix, unsigned *sampler_num)
{
        ScalingWeights horiz_weights = calculate_bilinear_scaling_weights(input_width, output_width, zoom_x, offset_x, BilinearFormatConstraints::ALLOW_FP32_ONLY);
        ScalingWeights vert_weights = calculate_raw_scaling_weights(input_height, output_height, zoom_y, offset_y);
        uniform_vertical_int_radius = vert_weights.int_radius;
        vertical_scaling_factor = vert_weights.scaling_factor;
        uniform_inv_vertical_scaling_factor = 1.0f / vert_weights.scaling_factor;
        src_horizontal_bilinear_samples = horiz_weights.src_bilinear_samples;
        src_vertical_samples = vert_weights.src_bilinear_samples;
        uniform_num_horizontal_filters = horiz_weights.dst_samples;
        uniform_num_vertical_filters = vert_weights.dst_samples;
        slice_height = 1.0f / horiz_weights.num_loops;

        // Encode as a two-component texture. Note the GL_REPEAT.
        glActiveTexture(GL_TEXTURE0 + *sampler_num);
        check_error();
        glBindTexture(GL_TEXTURE_2D, tex_horiz.get_texnum());
        check_error();

        tex_horiz.update(horiz_weights.src_bilinear_samples, horiz_weights.dst_samples, GL_RG32F, GL_RG, GL_FLOAT, horiz_weights.bilinear_weights_fp32.get());

        glActiveTexture(GL_TEXTURE0 + *sampler_num + 1);
        check_error();
        glBindTexture(GL_TEXTURE_2D, tex_vert.get_texnum());
        check_error();

        // Storing the vertical weights as fp16 instead of fp32 saves a few
        // percent on NVIDIA, and it doesn't seem to hurt quality any.
        // (The horizontal weights is a different story, since the offsets
        // can get large and are fairly accuracy-sensitive. Also, they are
        // loaded only once per workgroup, at the very beginning.)
        tex_vert.update(vert_weights.src_bilinear_samples, vert_weights.dst_samples, GL_R16F, GL_RED, GL_HALF_FLOAT, vert_weights.raw_weights.get());

        // Figure out how many output samples each compute shader block is going to output.
        int usable_input_samples_per_block = 128 - 2 * uniform_vertical_int_radius;
        int output_samples_per_block = int(floor(usable_input_samples_per_block * vertical_scaling_factor));
        if (output_samples_per_block < 1) {
                output_samples_per_block = 1;
        }
        uniform_output_samples_per_block = output_samples_per_block;
}

namespace {

ScalingWeights calculate_scaling_weights(unsigned src_size, unsigned dst_size, float zoom, float offset)
{
        // Only needed if run from outside ResampleEffect.
        call_once(lanczos_table_init_done, init_lanczos_table);

        // 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;
        int num_loops;
        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);
        }
        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);
        const int int_radius = lrintf(LANCZOS_RADIUS / radius_scaling_factor);
        const int src_samples = int_radius * 2 + 1;
        unique_ptr<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);
        float inv_scaling_factor = 1.0f / scaling_factor;
        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) * inv_scaling_factor - 0.5f;
                int base_src_y = lrintf(center_src_y);

                // Now sample <int_radius> pixels on each side around that point.
                float inv_src_size = 1.0 / float(src_size);
                for (int i = 0; i < src_samples; ++i) {
                        int src_y = base_src_y + i - int_radius;
                        float weight = lanczos_weight_cached(radius_scaling_factor * (src_y - center_src_y - subpixel_offset));
                        weights[y * src_samples + i].weight = weight * radius_scaling_factor;
                        weights[y * src_samples + i].pos = (src_y + 0.5f) * inv_src_size;
                }
        }

        ScalingWeights ret;
        ret.src_bilinear_samples = src_samples;
        ret.dst_samples = dst_samples;
        ret.int_radius = int_radius;
        ret.scaling_factor = scaling_factor;
        ret.num_loops = num_loops;
        ret.bilinear_weights_fp16 = nullptr;
        ret.bilinear_weights_fp32 = move(weights);
        ret.raw_weights = nullptr;
        return ret;
}

}  // namespace

ScalingWeights calculate_bilinear_scaling_weights(unsigned src_size, unsigned dst_size, float zoom, float offset, BilinearFormatConstraints constraints)
{
        ScalingWeights ret = calculate_scaling_weights(src_size, dst_size, zoom, offset);
        unique_ptr<Tap<float>[]> weights = move(ret.bilinear_weights_fp32);
        const int src_samples = ret.src_bilinear_samples;

        // 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);
        unique_ptr<Tap<fp16_int_t>[]> bilinear_weights_fp16;
        unique_ptr<Tap<float>[]> bilinear_weights_fp32;
        double max_sum_sq_error_fp16 = 0.0;
        int src_bilinear_samples;
        if (constraints == BilinearFormatConstraints::ALLOW_FP32_ONLY) {
                max_sum_sq_error_fp16 = numeric_limits<double>::max();
        } else {
                assert(constraints == BilinearFormatConstraints::ALLOW_FP16_AND_FP32);
                src_bilinear_samples = combine_many_samples(weights.get(), src_size, src_samples, ret.dst_samples, &bilinear_weights_fp16);
                for (unsigned y = 0; y < ret.dst_samples; ++y) {
                        double sum_sq_error_fp16 = compute_sum_sq_error(
                                weights.get() + y * src_samples, src_samples,
                                bilinear_weights_fp16.get() + 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) {
                bilinear_weights_fp16.reset();
                src_bilinear_samples = combine_many_samples(weights.get(), src_size, src_samples, ret.dst_samples, &bilinear_weights_fp32);
        }

        ret.src_bilinear_samples = src_bilinear_samples;
        ret.bilinear_weights_fp16 = move(bilinear_weights_fp16);
        ret.bilinear_weights_fp32 = move(bilinear_weights_fp32);
        return ret;
}

// Unlike calculate_bilinear_scaling_weights(), this just converts the weights,
// without any combining trickery. Thus, it is also much faster.
ScalingWeights calculate_raw_scaling_weights(unsigned src_size, unsigned dst_size, float zoom, float offset)
{
        ScalingWeights ret = calculate_scaling_weights(src_size, dst_size, zoom, offset);
        unique_ptr<Tap<float>[]> weights = move(ret.bilinear_weights_fp32);
        const int src_samples = ret.src_bilinear_samples;

        // Convert to fp16 (without any positions, as they are calculated implicitly
        // by the compute shader) and normalize.
        unique_ptr<fp16_int_t[]> raw_weights(new fp16_int_t[ret.dst_samples * src_samples]);
        for (unsigned y = 0; y < ret.dst_samples; ++y) {
                for (int i = 0; i < src_samples; ++i) {
                        raw_weights[y * src_samples + i] = fp32_to_fp16(weights[y * src_samples + i].weight);
                }
                normalize_sum(raw_weights.get() + y * src_samples, src_samples);
        }

        ret.raw_weights = move(raw_weights);
        return ret;
}

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, tex.get_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);
        }
}

Support2DTexture::Support2DTexture()
{
        glGenTextures(1, &texnum);
        check_error();
        glBindTexture(GL_TEXTURE_2D, texnum);
        check_error();
        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();
}

Support2DTexture::~Support2DTexture()
{
        glDeleteTextures(1, &texnum);
        check_error();
}

void Support2DTexture::update(GLint width, GLint height, GLenum internal_format, GLenum format, GLenum type, const GLvoid * data)
{
        glBindTexture(GL_TEXTURE_2D, texnum);
        check_error();
        if (width == last_texture_width &&
            height == 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, width, height, format, type, data);
                check_error();
        } else {
                glTexImage2D(GL_TEXTURE_2D, 0, internal_format, width, height, 0, format, type, data);
                check_error();
                last_texture_width = width;
                last_texture_height = height;
                last_texture_internal_format = internal_format;
        }
}

void ResampleComputeEffect::get_compute_dimensions(unsigned output_width, unsigned output_height,
                                                   unsigned *x, unsigned *y, unsigned *z) const
{
        *x = output_width;
        *y = (output_height + uniform_output_samples_per_block - 1) / uniform_output_samples_per_block;
        *z = 1;
}

void ResampleComputeEffect::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_x != last_offset_x ||
            offset_y != last_offset_y ||
            zoom_x != last_zoom_x ||
            zoom_x != last_zoom_y) {
                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_x = offset_x;
                last_offset_y = offset_y;
                last_zoom_x = zoom_x;
                last_zoom_y = zoom_y;
        }

        glActiveTexture(GL_TEXTURE0 + *sampler_num);
        check_error();
        glBindTexture(GL_TEXTURE_2D, tex_horiz.get_texnum());
        check_error();
        uniform_sample_tex_horizontal = *sampler_num;
        ++*sampler_num;

        glActiveTexture(GL_TEXTURE0 + *sampler_num);
        check_error();
        glBindTexture(GL_TEXTURE_2D, tex_vert.get_texnum());
        check_error();
        uniform_sample_tex_vertical = *sampler_num;
        ++*sampler_num;

        uniform_num_horizontal_samples = src_horizontal_bilinear_samples;
        uniform_num_vertical_samples = src_vertical_samples;
        uniform_slice_height = slice_height;

        uniform_horizontal_whole_pixel_offset = lrintf(offset_x) / float(input_width);
        uniform_vertical_whole_pixel_offset = lrintf(offset_y);

        uniform_inv_input_height = 1.0f / float(input_height);
        uniform_input_texcoord_y_adjust = 0.5f / float(input_height);
}

}  // namespace movit